Preface: American Civil War and "the rest" (Franco-Prussian and Austro-Prussian primarily) are two separate entities so ill discuss them separately even though it breaks chronological order. They involved two entirely different approaches of waging war and need to be treated as separate cases. The Americans had a Jominian (a Napoleonic military theorist) understanding of warfare and thus attempted to replicate Napoleonic methods tactically. When I get to this point at the end I'll describe Napoleonic tactics in it and you can use that to compare/contrast with what else I describe. The rest of the West, basically, Europe, would have a style of war which swung much more in the WWI-side of the spectrum in their respective Austro-Prussian and Franco-Prussian Wars.

The big game changers were breech loaded artillery (as opposed to muzzle loading), flintlock and percussion cap muskets (ie: using sparks or chemical pouches to ignite a muzzle loaded smoothbore or rifled musket) going to cartridge based breech loaded rifles, and proto-machine guns. The Austro-Prussian War would be the first (and last) European war where cartridge based breech loaded rifles were faced up against muzzle loaded muskets. The Prussians would enter the ring with the Dreyse Needle Gun. It would be a singleshot breech loaded rifle which had an effective firing rate of 8-10 rounds per minute and an effective range of over 650 meters. It had the added benefit as well as being capable of being fired from the prone position. The Austrians were using a percussion cap muzzle loaded musket called the Lorenz. It could not be fired from the prone position (by virtue of being muzzle loaded) and only had an effective range of ~500 meters. Most notably, however, was its firing rate; it could like all other muskets pump out 3 shots, 4 maximum, per minute.

The Dreyse completely and utterly outclassed the musket and through this many Prussian thinkers thought that 300 of their men were superior to a battalion of Austrians. They were completely right. This is how the Prussians fought in the Austro-Prussian War: They would send up a "skirmishing line" 2 lines deep. Remember in the ACW how men would be packed together elbow to elbow? Each man would be given a 3 meters between each of them -- 10 feet-ish a couple dozen men wide. Basically these 2 lines would approach the enemy and use cover as they saw fit and approached and retreated as they saw fit (again, infantry chains). The rest of the battalion would sit back and send in platoons/company's to reinforce the skirmishing line throughout the battle. That is, essentially, what WWI fighting was in the infantry realm of things. Skirmishing lines of men approaching an enemy position with strong reserves constantly reinforcing them in 'waves'.

The Austrians, in contrast, were heavily influenced by their very recent war with France in 1859 during the wars of Italian Unification. With the Austrians ranging their guns for long range (and thus firing "high" and letting the bullets drop) the French would use a revolutionary new tactic which the Germans would dub Stoßtaktik, or shock tactics. The French would essentially march at quick pace across open field to the Austrians face; while they would suffer casualties in the approach once they got in the Austrians face their muskets would still be "ranged" for long distance and thus would literally shoot over the French's heads. After being thoroughly routed in 1859 the Austrians, in their infinite wisdom, would just completely copy French tactics in their doctrine without any thought of it. That is, they would put their men in dense formation and charge in open field attempting to use 'shock tactics' against the Prussians in 1866.

The Austrians would, completely and utterly, be annihilated. As the Austrians were charging more or less shoulder to shoulder the Prussians were lying prone next to a tree or a rock or what have you and picking them off. At Podol 400 Prussians would face off against 2000 Austrians and they would, in the truest sense, obliterate them. The Prussians would have 100 killed or injured with the Prussians having over 1000 killed, injured, or captured. At Trautenau, one of Austria's few "victories", they would lose 5000 men compared to Prussia's 1300. The biggest battle of the war, the Battle of Königgrätz, saw 9000 Prussians killed or wounded with 43,500 Austrians killed, captured, or wounded. As you can see this was a war in which modern tactics and modern rifles would be the defining reason of defeat.

The Franco-Prussian War is an interesting case because it's one where the French had their own breech loaded rifle, the Chassepot. It was superior to the Dreyse Needle Gun in just about every single way and French infantry chains would, on average, outclass the Prussians. Where the Prussians had the distinct advantage would be in the strategic level of war (ie: mobilizing their men effectively and striking the French before they could 'get ready') and with their artillery, new breech loaded Krupp Guns. The French, despite their superior cavalry and infantry, would be hit immediately and taken by surprise. They would be battered back to Sedan where they would be surrounded on the ridges and simply battered into surrender.

The French still used muzzle loaded artillery which had to be set to detonate at set distances and thus the rounds had to be precisely timed to strike certain areas of the enemy at a certain distance. It was quite complicated and cumbersome at best. The Prussians breech loaded guns in contrast, while at a lesser range than the French, had a significant rate of fire advantage and also had percussion impact fuses which meant wherever the shell hit that's where it exploded. To make things even more deadly the Prussians made a habit of putting all of their artillery in one area and firing as a single empowered battery right at the front to obliterate the enemy. The French would be battered by combined German artillery while being squeezed from all sides by the infantry (despite the Germans suffering egregious casualties -- one Prussian company suffered 68% casualties at Mars-la-Toure for instance). A battle would look more or less like platoons/companies finding cover and picking off at each other with artillery batteries on both sides laying waste to the other side; very proto-WWI in my opinion.

We often hear about how WWI was a bloodbath because of inventions like the machine gun making centuries-old tactics useless,

A small point, but what changes in WWI is not the advent of the machine gun, but the much greater weight of field artillery and much higher force to space, compared to the earlier wars. In the early manoeuvre period, it is the field artillery that kills and wounds large numbers. The Russians lose to the Germans in the east not because of trenches but because the Germans have 105s everywhere and complete indirect fire systems. The French lose the battle of the frontiers because they adopt tactically offensive stances with their infantry and the Germans shoot them and shell them. German infantry attacks on the right wing always follow barrages, and if the defending infantry hasn't already been broken by them, then their attacks all fail. But defending rifle companies cannot stand in front of a WWI army above ground. They get shelled to death over a very short timescale.

There were a ton of military innovation during the 19th century.

Napoleon introduced light cavalry as a dedicated force attached to his armies - cavalry only intended for patrols, foraging, recoinnasance and keeping the enemy from doing just that. At the Battle of Austerlitz, the French light cavalry kept the Austrian and Russian commanders from knowing that his attacks on their flanks were feints and that he concentrated troops to break though their centre.

The French also introduced a corps organisation, where their army would march dispersed (as is an old axiom in military matters), but each dispersed part was a miniature army in itself, with light and heavy infantry, light and heavy cavalry and artillery - which mean that each corps could fight the enemy force and hold out until other corps could come to their aid.

The French also formed an advanced field medical service, including horse-drawn ambulances.

The French also introduced large standardised artillery parks, enabling them to use "grand batteries" of up to several hundred guns to devastate the enemy ability to form up.

The world exited the Napoleonic war with advanced infantry tactics (including assault columns), a corps system, advanced field medical services, dedicated light cavalry, new artillery tactics and above all conscript mass armies nationally recruited and manned rather than the mercenary/professional system that has been the norm before.

Rifled muskets started to become the norm in the 19th century, and with the invention of the minie ball, a rifled musket could be loaded with the same effort as a smoothbore one, and had the same rate of fire - but was far more accurate and had a far longer effective range.

Following this, the metal cartridge was invented, improving loading time and allowing rifles to become breach-loaders. Towards the end of the 19th century, the infantryman had gone from a smoothbore, muzzle-loaded musket with a rate of fire of perhaps 4-5 shots per minute (if he was well-drilled) with an effective range of max 200 meters and that required him to stand up to load to a bolt-action rifle that could fire 20 shots per minute with an effective range of max 1 200 meters and that could be fired and loaded lying down.

Artillery also turned rifled, and then breachloaded, then the cannons got a recoil system, alloing them to remain in place and thus be aimed at the same target after firing and increasing the rate of fire immensly. The range impoved to much that artillery towards the end of the 19th century needed forward observers equipped with longe-range communications equipment, since artillery now fired way beyond their own line of sight. Artillery also started firing explosive shells rather than roundshot, case shot and grape shot.

The telegraph and the raiload allowed a much improved system of communications, supply and transport for armies, allowing armies to fight together as a unit despite being far away from each other in a way that had not been possible.

Naval guns improved, firing explosive shells (just like land artillery) and ships started getting steam engines, making all sailing vessels completely useless. Then armoured plating appeared, doing the same with wooden ships.

Hot air balloons started to appear, being used for observation (for artillery) and recoinnasance.

Tactics started changing - the battalion stopped being the main unit of manouvre and rifle chains became the common way of fighting. Gatling gun type machineguns were introduced and started to replace ultra-light artillery as the support weapon of infantry, Cavalry became less about charging infantry and more about pursuit and recoinnasance.

If Alexander the Great had dropped by to visit George Washington, few things would have surprised him. Chief among these were big ships, gunpowder and movable type. But in the period between the American Revolution and 1899 lots changed.

To being with, cities were much bigger. Fewer farmers meant more young men available for bigger armies. These armies were fed on the beginning of preserved foods. Campaign season no longer really existed as soldiers did not have to worry about getting the crops in.

Next consider transportation. Steam opened up the American continent. Steam railroads for sure, but don't forget steam boats on rivers and at sea. Big armies and their supplies could move at greater speed.By the 1860s, whole armies could be shifted by rail on very short notice. Fewer and fewer places were protected from war by their isolation.

In the same way communications made huge advances. First better roads, then the telegraph let news move fast, and so those faster armies could jump from here to there. Napoleon was able to use his internal lines to move armies against his enemies defeating each one by one by one. In the old days, armies more or less stayed put.

Also society in general was much richer in 1899 than in 1799. More wealth meant more and better guns ships and whatnot.

So all in all, as Clausewitz said, war tended to expand and move toward totality.