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In broad terms, the answer is Operational Art.

In the Napoleonic concept of warfare, there were two levels: strategy and tactics. Strategy encompassed overall war aims, What your war was trying to accomplish. If you are Napoleon, that might be invading Russia through Poland to trap and destroy her army and force her to make treaty concessions. Tactics were the battlefield means of accomplishing those goals in a given battle, such as charges in column, or double envelopment. Battles were meant to be decisive, and fixed to a single point, geographically and chronologically.

In the words of influential German 19th century military theorist Carl Von Clauswitz,

The field of battle in the face of strategy is no more than a point; in precisely the same way the duration of battle reduces to a single moment in time.

Armies were relatively small, with limited firepower, and tactics required concentrating them. The goal of campaigns was to find, fix, and destroy them. But as firepower and the political reach of nation states increased over the 19th century, armies grew much larger and more capable. They had communications technologies that allowed orders to pass across entire countries instantly. They had transportation technologies, like railroads, that could move an entire army hundreds of miles in a single day. The fixed point started to broaden into a wide front. We can see this happening in the US Civil War, and in the Franco-Prussian and Russo-Japanese Wars, culminating in WWI, with the front in Western Europe extending from Switzerland to the sea.

The whole evolution of military art after the war of 1870 could be characterized as the transfer of combat decision from the front to the flank. This understanding became the basis for Schlieffen’s teaching. Thus, linear strategy strove even more to expand the front laterally. Schlieffen wrote: “It is the extended front that decides everything, facilitating envelopment and naturally presupposing a strong and numerous army....Modern battle comes down to the question of struggle for the flanks. The winner will be the one who deploys his reserves not behind the center, but on the extreme flank.” Such was the way that military art evolved at the turn of the twenti- eth century. In turn, the impulse to extend the flanks and to extend the front required an increase in the size of armies. Their growth was well ensured during the epoch of imperialism. By 1914, the Germans maintained an army of two million, a number surpassing that of 1870 by four times. The essence of competition among capitalist military systems before the war of 1914 lay in the greatest possible extension of flanks in order to achieve an enveloping position. -Isserson, The Evolution of Operational Art

However, faced with this extended, static Western Front, offensive planners were largely still operating under Napoleonic principles. They sought to break this broad front by finding a weak point, and exploiting it tactically. It was a battle centric approach to war. Erich Ludendorff, Germany’s most important WWI general, and the hero of Tannenberg, said, “Tactics ought to be placed before strategy.” This was an accurate characterization of both sides’ approach to the stalemate you describe on the Western Front in WWI. It was a constant search for a weakness in the defensive lines, which could be exploited tactically. Offensives centered on this concern, rather than on what gains could most advance strategic goals. But at the same time, the technological advances that had broadened the front enabled a mobility that held the key to breaking it. Improved transportation and communications could strengthen the offense, as well as the defense, but it required a new approach to offense. An approach that considered not just the breadth of the front, but its depth, and attacked in coordinated operations from multiple directions, and at multiple levels. This was a gap between the concepts of strategy and tactics, called operations. And the theoretical framework behind it was Operational Arts.

Operational Arts were first identified by a clique of influential Soviet generals between the mid-1920s and late 1930s. Between them they developed a comprehensive framework of operations, around a concept called Deep Battle. Deep Battle dispensed with linear tactics, and the pursuit of a decisive battle through envelopment (flanking). It did not seek to turn the enemy’s flank wherever it was easiest, like the race to the sea at the beginning of WWI. Instead it implemented a system of inter-related battles, designed to execute a specific strategic goal. Attacks were deeply echeloned, and with the aid of mechanization and aviation, directly attacked the interior of the defense, not just the front line. Today, the most influential of these Soviet theorists is Georgi Isserson, and it was his version of the Red Army Field manual, and his theory of Operational Arts, that defined Deep Battle in WWII.

Now, the Western Allies in WWII had no concept of operational art, or even of Deep Battle. But they did practice operations. Operations is frankly what Eisenhower was famous for. Normandy was chosen not merely because it was tactically advantageous. There were numerous tactical issues with it. But it offered operational advantages, not least that it was geologically and meteorologically similar to the western English coast, which meant that realistic training was possible, and problems could be worked out beforehand. They wanted no repeat of Dieppe. No surprises. And Overlord was a massive operation of coordinated attacks, not just on multiple beachheads by multiple armies, but in depth. Air forces intensely bombed German targets dozens of miles from the beaches. Airborne troops, 13,000 of them, landed behind German lines, to cut reinforcements off from the beachheads, and crucially, from the port city of Cherbourg. Even where they weren’t attacking, the allies conducted diversionary operations, such as dropping paradummies, fake paratroops, to confuse the German response. Overlord was not a battle. It was a large scale coordinated operation comprised of numerous battles, fought across a broad and deep front, from land, sea and air, designed to reenforce each other and accomplish well defined strategic goals. This kind of operation was enabled by further development of the technologies that had previously broadened the front and ground battle centric offenses to a halt. Mechanization, communications and firepower were the answer to broad static defenses, just as they had been its original cause. Tanks, trucks, planes and radios enabled freedom of penetration in the attack. But only with careful operational planning. Operational planning gave offense back its mobility.

By the end of WWI, both sides had developed effective tactics for attacking static linear defenses. What they lacked was a framework for turning tactical success into strategic accomplishments. Hence Germany’s Operation Michael, in 1918, which produced great success in battle, achieved no strategic gains at all. In the words of Lt. Col. Thomas E. Hanson, Director of the US Army Combat Studies Institute (in his Forward to the Army’s translation of Isserson),

Prior to the Great War, no army in the world possessed a codified body of thought that enabled senior military commanders to visualize the aggregate effects of tactical engagements across time and space. By 1918, after a dramatic revision of drill regulations into something approaching true doctrine, the German army was furthest in realizing this goal. Ultimately, though, the Germans could not translate tactical success into strategic victory because they could not resource military operations in sufficient depth to render local successes decisive. Understanding that the character of warfare in 1918 was radically different from 1914 would have enabled Ludendorff to see the flaws in the MICHAEL offensives and perhaps mitigate them. And although the interwar German Army spent a great deal of effort reflecting on the lessons of 1914-1918, German understanding of the operational art remained incomplete.

Or as Isserson described it,

In sum, the question boiled down to the following: offensive combat during the World War was generally waged along a front line of direct contact, while the defensive depths remained untouched. Tactical echelon- ment in the offensive served only to reinforce and restore attacking units. Although the tank changed this situation, deep allied echelonment for breakthrough development remained embryonic and played no essential role. Meanwhile, the defense retained full freedom for concentration of fresh reserves within its operational depths. The dominant feature in offensive combat during the Great War was that the combat was waged along a single line of direct contact, yielding what amounted to one-dimensional linear combat. Deep echelonment of the combat formation failed to change this phenomenon because deep attack echelons were assigned only to reinforce the combat front line.

First let me preface this answer by saying I am more versed in the First World War than I am in the second, but I feel like I can adequately answer this question. Let's start with some observations about the question itself/our broader view of both WWI and Normandy. It is worth noting that many WWI battles and engagements did not fall into the category of "full frontal charges" into defended enemy positions, despite our popular conception of the war and how it was fought. As the war continued, it became less and less likely for forces to engage in such actions on the Western front, especially as infantry and combined arms tactics began to evolve into something more sustainable and effective. (The notable exception being the Americans, who upon their entry into the war in 1917, patently refused to listen to the advice of other allied forces and continued with brutal frontal infantry assaults.)

Turning to Operation Overlord, we must again defy our popular perception of the battle and acknowledge that not all of the beaches were equally deadly and heavily defended. American popular culture and collective memory in particular envisions D-Day purely in terms of the bloodiest beach, Omaha, but tend to put aside the fact that other beaches, such as Utah, Gold, and Sword were nowhere near as brutal or as well-defended.

However, I feel as though this question is specifically aimed at the popular perception of both the WWI Western Front and D-Day, so for the purposes of this answer I will compare to “archetypical” battles (or at least the first day of each): The Somme and Omaha Beach. Both are incredibly bloody assaults (the Somme far more so), relatively straightforward, and define popular perceptions of their respective conflicts up to the modern day. I will skip any preamble about the battles (they’re famous enough to assume at least some level of popular knowledge of how they arose) but I will give a brief overview in terms of casualties and pre-assault preparation. We’ll then move into a comparison of a series of factors that contributed to the relative success of Omaha infantry assaults as opposed to the relative failure of the same at the Somme.

The Somme: The battle opened on July 1st, 1916 following an artillery bombardment that had lasted almost a week and consumed some 1.5 million shells. 19 Allied divisions (13 British, six French) assaulted six divisions of the Germany army heavily dug in across no man’s land, which usually consisted of a couple hundred yards of “open” ground, in a largely straightforward infantry assault. The results of the first day attack were disastrous for the Allies. Minimal gains were obtained in return for 57,470 British casualties, including 19,240 dead. The Battle of the Somme continued for 141 days, resulting in an Allied victory and German withdrawal at the cost of over 420,000 British and 200,000 French casualties.

Omaha Beach: Part of the wider Operation Overlord, a series of coordinated landings on the Normandy beaches of France. Two US divisions alongside nine companies of Army Rangers amphibiously assaulted a five mile section of heavily defended beach. An artillery and aerial barrage proceeded the assault on June 6th, 1944, which were initially meant to consistent of a combined arms assault but quickly degenerated into a largely infantry based advance. At the end of the day, American forces had made minor gains, allowing for the subsequent collapse of the defenses in the following days. The gains cost 2,400 American casualties, the highest count of any of the beachheads.

Now, why were the Americans, approaching into the jaws of death, able to succeed were so many British units failed at the Somme? Let’s look at a list of factors for comparison.

1. Terrain

The terrain across the Somme front varied to some degree, but in the main it was largely flat, slightly rising land between the two lines. After days of artillery shelling, some of no man’s land was a mangled hellscape. The Queen’s Victoria Rifles, “moved forward in long lines, stumbling through the mass of shell-holes, wire and wreckage…” At other parts of the line, the British infantry found themselves advancing across relatively unbroken terrain, more akin to a football pitch than a battlefield. The 13th Yorkshire and Lancasters advanced across “a long grassy slope rising gently to a series of low crests about six hundred yards in front.” The “Newcastle Commercials”, as John Keegan reports, were confronted with terrain that allowed them to advance “following a football kicked by a well-known north country player”. Unlike many other parts of the Front, the ground on the Somme drained well, making it slightly less of a mud-choked mess than its famous equivalents. Shell holes would eventually become a part of the landscape, but as of the first day, they were not as present, making it impossible for advancing infantry to find any sort of cover as they advanced, often hundreds of yards, into the teeth of concentrated and layered German fire. In those parts of the line where the Germans occupied heavily fortified villages, the situation was much the same.

Comparatively, Omaha Beach’s terrain was much more favorable to an infantryman. It seems ridiculous to say, but it is undeniably true. Most infantry landing on Omaha Beach occurred slightly after low tide, forcing the Americans to advance roughly three hundred yards (give or take) across relatively chaotic ground covered with scatterings of debris from defensive works until they reached the shingle and sea wall, which provided adequate cover from the small arms fire of the German defenders (if not from the German mortars and artillery). From the shingle/sea wall, it was another 200 yards across relatively open sand to the base of the cliffs. At the base of these cliffs Americans could once again largely take cover from enemy small arms fire and from enemy artillery, though not necessarily from mortars or grenades dropped from above. A number of small “draws” or valleys offered access to the clifftops from the beach, but these were the most heavily defended parts of the line.

On balance, the infantrymen advancing across Omaha Beach had a much better chance of reaching adequate cover from the main killer of both Omaha and the Somme (discarding artillery): the machine gun. There was little opportunity for a British soldier on the gently rising slopes of the Somme to do anything when faced with “a stream of bullets so dense that no one could walk upright across the front of the machine-gunner’s position” whereas the Americans at Omaha could, if they were able to move those three hundred yards through the debris of the beach, reliably count on the shelter of the shingle to take them out of the line of fire from the machine-gunners above. This in turn could give them crucial time to regroup, plan, and prepare for different avenues of assault. The cliffs as well allowed for different means of attack as opposed to the Somme line, in which infantry once committed had little time to stop and plan or consider alternative routes of attack. The only option was to go forward or risk death in an open field. The time bought by the cover of Omaha was a key part of allowing the Americans to better reorganize orchestrate the small unit assaults that actually achieved the breakthroughs on the day of the landing. Few British soldiers on the Somme were quite so lucky.

If I have read your question correctly, you’re asking how the difficult terrain within the Normandy beachhead (i.e, the hedgerows, or bocage) paired with modern weaponry did not lead to static warfare within the beachhead or on the Western Front in general. The short answer is that, frankly, the US Army (which fought through the bulk of the bocage) in many ways did get demolished, particularly early on, and it was only through a healthy supply of replacements and rapid lesson-learning at all levels that American forces were able to develop a system for hedgerow busting, the employment of which ultimately allowed them to fight their way out of the swamps behind the beaches and onto terrain more conducive (though the best was in the Anglo-Canadian sector) to mechanized warfare. From these positions, along the St. Lo- Periers road, First US Army was able to execute Operation COBRA, which crushed the left flank of German Seventh Army and led to the collapse of the German cordon around the beachhead.

For those that are unaware, a distinct feature of the Norman countryside is the hedgerow. The result of centuries of cultivation, the hedgerows were originally grown as fences to mark boundaries between fields; they are quite formidable, stretching up to fifteen feet tall with a dirt base that can be as tall as five feet. Typically they are 2-4 feet wide, and all but impenetrable. The fields they demarcate are fairly small, only a few hundred yards long and wide, and openings are few. They are not a local problem, either, as they cover essentially the entirety of the Cotentin peninsula and extend inland behind the invasion beaches for a few dozen miles. They are an absolute nightmare for a mechanized army to attack through, as they prevent armor from maneuvering cross-country, and are natural defensive strongpoints. It is not hyperbole to say that a handful of infantry with one or two AT guns, some handheld antitank weapons, and a machine gun or two can hold off a combined arms force several times their size, as the armor can’t maneuver, the infantry can’t maneuver, and even with aerial observation applying effective artillery fire against the defenders is a challenge. The US Army knew about the hedgerows before they landed in France, but completely and totally underestimated the difficulty that they presented to forward movement, to the point that they made no plans for how to attack through them. Thus, when the amphibious landing portion of OVERLORD transitioned into the “expand the beachhead” portion, the units attacking into the bocage were hit incredibly hard by the German defenders dug in there, partially because tank-infantry training was, to understate the problem, lacking, and because nobody had really looked at the problem that the hedgerows presented.

The level of training and proficiency that First US Army possessed is relevant to this discussion. With training in England focused on amphibious maneuver and reducing beach fortifications the bulk of the infantry divisions involved in the initial echelon didn’t really address tank-infantry training; this was made worse by the late attachment of tank battalions to the divisions. Only four of the initial eleven divisions committed had any combat experience; the 1st Division would land on Omaha Beach on D-Day, the 9th Division would be a follow-on unit at Utah Beach, the 2d Armored Division would be a follow-on unit at Omaha Beach, and the 82d Airborne Division would land behind enemy lines on D-Day. The remainder of the army was green, though generally well-trained; this varied according to the caliber of leadership each possessed, though the 90th Division would stumble largely because its leadership was entirely useless in combat, rather than as a result of bad training. In short, the bulk of these units were trained perfectly well as far as the bullet-points go, but had not yet been through the most critical test of all, which is combat itself. Unfortunately, the lack of emphasis on tank-infantry coordination in training would come back to haunt First Army, as the terrain constraints of the bocage demanded close and constant tank-infantry operations in order to beat the defenders over the head with the firepower necessary to allow infantry to maneuver and close on hostile positions.

When the Allies finally did land in France and attempted to move inland the bocage wreaked havoc on the attacking American forces. Tanks and infantry constantly outran each other for lack of coordination and understanding of how the other fought, tank commanders sent their armor streaming down the narrow roads in the hedges only to take heavy losses from concentrated AT weapons, and little ground was actually gained in exchange for exorbitant losses. The 4th Division alone, which incurred only 200 casualties on Utah Beach, suffered nearly 100% turnover in its rifle companies in its first three weeks ashore, taking over 5,000 casualties for the month of June as it attacked toward Cherbourg. This was a pattern that repeated itself, literally, for weeks, as the intensity of the combat ripped junior leadership to shreds and replacements streamed into the infantry battalions. All the while leadership at all levels scratched their heads at the problem, trying to find a way to reduce losses while maximizing gains and casualties incurred by the enemy.

The solution to the problem of the bocage came at the lower levels. Each division devised its own way of attacking hedgerows, though the concept was universal. A maximum of firepower had to be employed in the assault, and to do that, infantry and armor had to be concentrated; rather than assigning a given unit a frontage in yards it was assigned a frontage measured in fields. To effectively employ armor it had to be moved off the easily defended roads; so engineer support or modification of the tanks themselves was necessary to destroy hedgerows and allow the tanks access into the fields. Massing firepower was not enough, it had to be employed effectively, which meant that close coordination between infantry, armor, artillery, and engineers was required; thus infantry officers were mounted in tanks, telephones were mounted on tanks, infantry radios were installed in tanks, and hand signals and tracer ammunition were utilized for signaling between infantry and armor. Planning took on a critical role, with each attack taking on the characteristics of a miniature set-piece battle: every unit in the action was to know its place, what it had to do, and how its conduct affected the course of the battle.

The result of these efforts led to big gains at reduced cost, “big gains” being two or three fields in a given attack. Some outfits preferred to lead with armor, others with infantry, but generally speaking the attack opened with the destruction of a hedgerow. Infantry and armor would breach the hedgerow in multiple points as armor suppressed the opposite hedge with machine gun and cannon fire; mortars and artillery would fall in echelons behind the enemy position to prevent his withdrawal intact and disrupt the forward movement of reserves. As armor and machine gun teams suppressed the hedgerow the infantry would sweep forward, methodically destroying enemy antitank teams positioned in the hedges on the flanks. A handful of riflemen remained near the armor at all times to provide local security. As the attack progressed armor would advance into the field but it was the infantry that would clear the enemy hedgerow. Once this was accomplished the attack would reset and the next hedgerow would be taken the same way.

There were variations on this scheme. German defenses were deployed in depth; the first hedges were a beefed up outpost line, and behind it was a defensive zone comprised of belts of prepared positions. The Germans quickly realized that most attacks were preceded by artillery and reacted accordingly, which led battle wise formations to forego artillery preparation or infiltrate as far forward as possible to the outpost line during the night. In the latter scenario the attack would usually kick off without a preparation in order to surprise the enemy, overcome the outpost line, and attack the primary defensive lines before the enemy had time to react.

In this fashion the US Army slugged its way through the difficult terrain behind the beaches and up onto dry enough ground to launch COBRA, which avoided stalemate on the Western Front and began the collapse of German resistance around the Normandy beachhead.

They didn't charge through it at all. The hedgerow battles in Normandy well known for being a grind it out slugfest in which the Allies took ground one small section at a time.

But if the question really is how they advanced and why they were able to compared to WW I, the first thing that comes to mind is the maturation of the tank. Towards the end of WW I the value of the tank in breaking defensive formations was first put into action. While tanks didn't have a strategic impact in WW I, in several tactical battles they proved the concept that mechanized armor could play a decisive role in breaking through entrenched defenses. By WW II of course, tank development had come a long way. The development and availability of armor formations made WW I style defensive tactics less effective. Of course Normandy was not ideal tank country, but the tank working in concert with infantry was a tough combination for the defender to counter, particularly when the attacker has vast material superiority.

However it's also the case that the defenses that the Germans had in Normandy were nothing like the trenches they had in WW I. The lines in WW I were largely static and lasted for years, which allowed the Germans to build truly incredible defensive works. Trenches with underground bunkers reinforced in concrete, with pill boxes and fields of fire established well in advance. Usually there was a secondary and tertiary trench in the event the first trench was overrun from which German forces could launch attacks under the cover of their own artillery, often while much Allied artillery was unavailable due to it needing to be moved up and re-sighted to keep up with an advance. All these factors, and no real answer to the machinegun until the tank, made offensive operations very difficult.

Back to the Allies in Normandy, another huge advantage they had was air superiority in a war where air power was extremely important and effective when used properly. Compare that to WW I where air power was a factor, but still in its infancy, and for most of the war neither side had true air superiority to the extent that it could be decisive on the ground combatants. Allied air power played havoc with the Germans during the Normandy battles, making it difficult for them to concentrate forces and bring up reserves.

I would also argue that the German forces facing the Allies in Normandy were not as strong as the German army for most of WW I. The Germans had good units in France with good kit, but they also had some fairly substandard units that masked their numerical and qualitative weakness in France. By Normandy the Germans had suffered enormous losses and, while not at the end of their rope, they were starting to scrape the bottom of the barrel in terms of manpower. While this was a problem for Germany at the end of WW I, I would argue that for most of the war they were better manned on the Western Front than they were in Normandy in 1944.

tl:dr: The allies didn't charge through, it was tough. But what helped them was the tank, air superiority, and a weakened German army that was not "dug in" in nearly the same way that the German army was in WW I.

A good book on the Normandy fighting is Zaloga's, Armored Thunderbolt. This is a book about the Sherman tank, but it also goes into great detail about the nuts and bolts of US forces fighting in the bocage, and the role of infantry and armor (German and US) operating together in this area.

Well, there are a lot of differences, especially technological, that changed warfare drastically between the conflicts: I would argue the largest factors being advances is Air Power, and communication.

Soldiers in WW1 didn't have the benefit of close air support. Air power was almost entirely used for reconnaissance, spotting, etc. It's true that some truly massive bombers being built and deployed during this time, but the capabilities and targeting abilities meant their effect was minimal.

In WW2, you've got close air support. If there's a machine gun nest that's a problem, a platoon leader can easily (relatively) communicate with his chain of command, and get a bomber there to accurately eliminate the threat.

In WW1, radio communication was SLOW. A platoon hits a snag on an advance, he has to send a RUNNER with the info. That runner can get killed easily, get sidetracked etc. By the time the runner reaches some sort of commander, most likely the tactical situation the message was about is already very old information, and breakthroughs can't be exploited, and hold-ups can't be addressed. Adolf Hitler was a dispatch and order runner. These activities are what got him promoted and decorated because it WAS a very difficult and important job. Eventually, during the last bit of the war, communication got better, and we see radio technology advance rapidly (as does technology in general rapidly advance in WW1).

In WW2, we've got portable radios. Information can be relayed in real time. A commander's knowledge of a tactical situation is much more comprehensive, and they're able to react in a much more rapid fashion. Radio communication, in my humble opinion, probably has had more of a direct and important effect on war than any gun ever designed by man, or ever will be.

So, to address your scenario, if the Normandy invasion was made in 1917, it absolutely fails. It would be just as awful as you can imagine, but honestly to the poor boys involved it would've been just another futile advance out of hundreds of futile advances.

In 1944, a platoon commander, in real time, can tell his regimental commander "get me some help, there's a machine gun nest at this exact position" and that commander can just organize that and send it. And a plane can come and wipe it out, because planes have that ability now. They're more effective due to radios, too.

In 1917, the runner that platoon commander either gets there hours later, or is dead in a ditch. Help most likely isn't even necessary anymore.