As early as the North African campaign the allies had encountered the Tiger And 88 millimetre gun which terrified Allied soldiers. Throughout the French campaign the allies mainly relied on the Sherman which was completely inadequate to match the German Panther or Tiger. The British only introduce their best tank of the war the comet, in early 1945 when the war was drawing to a close, same thing with the Americans with the m26 Pershing. What took the developed of tanks so long?
It didn't. the Sherman was more than a match for the Panther. According to the U.S. Army Balistic Research Lab study of the engagements of the 3rd and 4th Armored Divisions the Sherman scored a 3,6 to 1 kill ratio against Panthers. The Sherman is more maneuverable, faster, has better sights, fires faster and is much more reliable than the Panther. While it technically has thinner armor and a weaker main gun that really doesn't matter too terribly much, it is more than enough to penetrate anything but the front of a Panther and it's superior mobility, sights and rate of fire allowed it to do just that.
This whole myth is incredibly frustrating and based in a misunderstanding of how armored combat works. Yes, if a Sherman and a Panther were to stand face to face in an open field and just slug it out the Panther would win every time but in reality the faster and more reliable Shermans were generally able to capture key ground faster than a panther, allowing them the advantage of waiting in a prepared position almost every time. Their superior sights and maneuverability also allowed them to shoot at the rears or side of panther most times.
The panther is a decent enough tank for the very specific purpose of slugging it out with another medium tank in a head on battle. It preformed better in the open fields in the east than ever it did in the west but it has a very limited zone of immunity (so does the Sherman to be fair) but the sherman has so many other advantages that ultimately far out-weighed the thicker armor and bigger guns of the German tanks.
The question might as well be flipped on its head. For the greater part of the war, the Germans were fighting at a technological disadvantage, with their rank and file tanks being inferior to the tanks of their opponents.
Let's start at the beginning of the war. In the fight against Poland, the Germans were, at the very least, at technological parity. Polish light tanks had armour and armament a little worse than German medium tanks, but remember that medium tanks made up a very small percentage of German forces. Only 21 PzIII tanks and 198 PzIV tanks entered Poland out of a total armada of 2553, the rest were light tanks like the PzI that was obsolete even during the Spanish Civil War and the PzII that was hardly any better. The armour of these tanks, including the medium tanks, was easily overcome by Polish 37 mm and even 20 mm guns.
Next year, in France, the German forces had not improved significantly. The proportion of new tanks increased, but their protection and firepower did not. The French had much more heavily armoured tanks than the Polish army did. Even their light tanks boasted 30-40 mm of armour, not an impenetrable barrier for German 37 mm guns, but still quite significant. More modern medium and heavy tanks were more than a match for the Germans. Famously, during the Battle of Stonne one Char B1 tank took 150 hits from German artillery, none of which penetrated. The tank's commander, Captain Pierre Billotte, claimed 13 tanks and 2 German guns that day, not to mention other vehicles.
Little changed in 1941. The front armour of the latest PzIII and PzIV models was now thicker, but even these new tanks had weapons that were only effective against Soviet light tanks, not the new T-34 and KV that entered service two years prior. Indeed, the PzIV with its low velocity gun and leaf spring suspension was closer to the positively ancient T-28 tank than the T-34. The majority of the tank force was still relying on outdated light tanks and "booty panzers" looted from occupied nations. Even unreliable and worn out British cruiser tanks that were captured at Dunkirk were pressed into service, to rather poor results. To quote Forczyk: "If any word described the state of German tank design at the start of Barbarossa, it is mediocrity."
In 1942, like you mentioned, there was a new super-tank on the block. This wasn't the Tiger, though, this was the Sherman. This tank was superior to the PzIV in every way, except firepower. The Germans did upgrade the PzIV with a longer barreled gun, but this came at a cost. The chassis was overloaded. No further upgrades could be made, while the Sherman was in the prime of its life and would get significantly heavier before the end of the war, obtaining a larger gun, a more powerful engine, and wider tracks. You're right that the Tiger was introduced in North Africa, but these tanks were available in incredibly small numbers, while the Allies already had weapons capable of killing them available en masse: these were American 76 mm guns and British 6-pounders and 17-pounders. The Red Army was also not without a Tiger-killing weapon. Much like the German Flak 36, the Soviet 52-K 85 mm AA gun was used to great effect as an anti-tank gun. Indeed, even before the Tiger was known, the Allies already had ways of dealing with it. In 1943 these weapons became available on the chassis of medium tanks (SU-85, T-34-85, Challenger I, 76 mm armed Sherman tanks). These tanks were available in very large numbers by 1944, much larger numbers than Tigers could be built in.
One can argue that in 1943 the Germans finally obtained an edge over the Allies in terms of a general purpose tank in the face of the Panther, but it was still vulnerable to 17-pounder guns and even lower velocity American 76 mm guns. As /u/Superplaner pointed out already, Shermans proved more than capable against a theoretically superior foe. The American and British didn't ship anything bigger to the mainland arguably because they didn't need to.
Sources:
http://tankarchives.blogspot.com/2017/01/pzkpfwiv-ausf-through-c.html
http://tankarchives.blogspot.com/2017/07/pzkpfwi-ausf-b-all-grown-up.html
http://tankarchives.blogspot.com/2016/10/renault-r-35-more-for-less.html
http://tankarchives.blogspot.com/2015/06/world-of-tanks-history-section-stonne.html
http://tankarchives.blogspot.com/2016/05/cruiser-iv-bit-more-armour.html
R. Forczyk, Tank Warfare on the Eastern Front 1941-1942
We need to remember something about these big tanks like the Panthers and Tigers: we beat them before Normandy. We beat these heavy tanks in North Africa and Sicily and the US Army did have the 75 mm gun Sherman. So why didn’t they get a bigger gun or a heavy tank sooner? They didn’t need it at the time, they were beating these heavy German tanks before, so why change anything? Well the terrain in Normandy and Western Europe was a bit different and favored the defender. The Panther while a good tank has a lot of problems unless used correctly. The Panther’s development was rushed whether scared of the T-34 or for Operation Citadel, the production was rushed and a lot of problems were in the tank. These problems would stick with tank for its entire life. But if used in a defensive position where they could ambush tanks and didn’t have to move too far it could be a great tank.
The Tiger wasn’t that prevalent as we think it is. The production line ended in August 1944 and only about 1100 were produced in its 2 year production. The US army only reports that they encountered in Mainland Europe the Tiger 3 times. While they encountered the King Tiger more often than the regular Tiger. The tanks or AFV it usually encountered was the Panzer IV, which made up the majority of tanks in the German Army, then the StuG assault gun which was Germany’s most produced AFV. These tanks could be beat by the 75mm Sherman tank.
While the Sherman has its shortcomings they did try to fix the gun. Like producing a larger gun on their Sherman with a 76mm gun. The Sherman has great reliability, produced in large numbers, light enough to be transported in large numbers so not only tank division had them, but infantry had them as support. And most importantly crew survivability, we tend to think the Sherman is a death trap, but the reality is it wasn’t. It had spring loaded hatches for 4 out of the 5 crew hatches, meaning if the tank was on fire it was much easier to get out of the tank. Alongside the fixing of ammunition stowage, which decreased burn rates deaths to non existence.
The Sherman was a good tank that has had a bad press team. The Sherman competed with the big cats and did come out on top in the end.