If you have any specific questions ask and I'll help you out there!
Let's start with the Austro-Prussian War. The Prussian's enter the ring with the Dreyfus Needle Gun, a breech loaded bolt action rifle, which could fire 8-10 rounds per minute which could be loaded and fired from the prone position as well as having an effective range of over 650 meters. The Austrians in comparison were using a muzzle loaded rifled musket called the Lorenz. This could not be fired while in the prone position and while having an effective range of 500-550 meters which could contend with the Needle Rifle was dwarfed in firing rate. Again, 8-10 rounds per minute for the former but the latter would be lucky to get 4 out, maybe 3. Add into that the flexibility of the Needle Gun (firing from prone, much more reliable, etc.) and 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. Basically because both sides used muzzle loaded muskets in that war the French decided if they could rapidly charge the Austrians during their significant reload times, even if they ate the casualties, the Austrian weapons would still be sighted for long ranges (which makes their guns shoot high) and the Austrians would just straight up miss once they got close. It worked amazingly well. The Austrians would dub this Stoßtaktik, shock tactics, and it was the central idea of their military theory going into the Austro-Prussian War just 7 years later. The Austrians would, completely and utterly, be annihilated by the Prussian forces. They would charge in dense formations in their "shock tactics" and would try to use their cavalry to support these charges. Both of which would melt under Prussian infantry chains at significant range before they could inflict any casualties. 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 Austrians 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.
The Franco-Prussian War was an interesting war because it was one where the French had every advantage in regards to infantry but a distinct disadvantage with artillery and operational and strategic command. In response to the Needle Gun they standardized their own breech loaded rifle, the Chassepot. It shot faster, more accurately, and over further distances than the Needle Gun to a noticeable effect. We see throughout all the early battles the French absolutely slaughtering the Prussian forces even with distinctly less men present. Entire Prussian columns would be held up by a few dozen men at times while their cavalry charges would melt under rifle fire. These battles were truly the end of the age of shock cavalry. The reason the French lost so horrendously was not an issue of tactics but more of an operational one, as I do feel this bears mentioning. The Prussians were capable of mobilizing a massive force much quicker than the French and basically pounded them into encirclement at Metz and then Sedan. The French simply did not have the time to react in time. With that said though, the Prussians did have a distinct advantage in the artillery department.
*In the woods and close country which lay before the French positions the temptation to 'get lost' was sometimes overwhelming. Only close order could give the infantry confidence, and close order in the face of breech-loading rifles was suicidal. The answer to the problem, as the Germans discovered during the course of the campaign, was for the infantry, so long as its armament was inferior to that of the enemy, to hold back and leave matters to the guns; and the German field artillery proved quite capable of settling matter itself. Its range and rate of fire gave it, at the beginning of both battles, such an ascendancy that the French gunners -- including the dreaded mitrailleuses^[1] --were silenced in a matter of minutes.*^[2]
It was ultimately German artillery which won the day for the Germans and how most battles in the Franco-Prussian War were determined, at least the significant ones. The French would entrench themselves and attempt desperate cavalry charges as they were surrounded but could not contest the Prussian artillery. 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, however, had breech loaded artillery which, 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). Eventually, after being operationally and strategically outplayed the majority of the French army and Napoleon III would be forced into encirclement at Sedan and, with no hope of breaking out, would surrender and thus the de facto end for the French.
TL;DR:
1866 Austro-Prussian War: The Austrians replicated what the French used successfully against them in the Italian Wars in 1859. That is, they sent densely packed columns in rapid charge against loose Prussian rifle chains / skirmish lines using breech loaded rifles; as you imagine it went horribly. I would also observe this is one of the only cases in history that I have studied where a clear technological and tactical doctrine advantage is achieved between Western powers.
1870/71 Franco-Prussian War: The French would be on par if not superior to the Prussians in many respects in the realm of infantry and cavalry. The Prussians however would operationally and strategically outplay the French by mobilizing so rapidly the French would not have time to react in any meaningful way. Even despite high Prussian casualty counts they would strike so rapidly the French would be beaten back in successive losses and eventually (and quickly) encircled. Because of the encirclement the Prussians used their superior (technologically and doctrinally used) artillery in 'batteries' which basically pounded away at the surrounded Napoleon III (along with the rest of the army) and causing the eventual white flag.
Notes:
^[1] Mitrailleuses were proto-machine guns which could fire up to 200 rounds per minute.
^[2] Howard, Michael, The Franco-Prussian War: The German Invasion of France 1870-1871, pp. 118