Well, there are a lot of ways to answer that question, so, let me take a stab at a few of them.
The most basic answer is, "Not too much." Most professional officers- ones that would have had extensive military educations before the wars- would have studied Wagram and it's surrounding campaign (Landshut, Aspern Essling) as part of their education, either directly, or indirectly, though the works of du Picq, Jomini and Clausewitz. Even today, at West Point, the mandatory military history class starts no later than Napoleon, and would include a discussion of Wagram.
However, if we expand beyond this, we can see, in Wagram, the development of something that will be very important in fighting those wars: military command organization and structure. Both armies in this battle- for the second time in history- use the Corps d' Armee system developed by the French earlier in the Napoleonic Era. The Corps d'Armee system is a way of overcoming one of the biggest obstacles in army command before the Napoleonic era: human cognition. Most successful armies- from the Romans to NATO- use a unit of 700-1200 men as their basic unit of maneuver. Average commanders can juggle between 20 and 30 of these units at once, practiced ones might handle 40, geniuses 50. In fact, a lot of military genius in history can be attributed to a general who can just handle more units in his head at once. For this reason, you'll see most field armies, before the Napoleonic era, clustering in size from between 20,000 men and 50,000 men. It's just the size of an atmy one man, with a small staff, can keep track of easily.
If the army gets bigger than that, before this era, there are a couple of common solutions. One is that the commander just ignores part of the army. He takes charge of whatever his head can handle, and that force is going to be the main attack, or defense, or flanking manuever, or whatever. Everyone else just kinda fights what's in front of them, unless and until the chief moved his attention in that direction. The second possibility requires a good and trustworthy subordinate or series of subordinates- one is not particularly common, more than one is vanishingly rare. This subordinate can be trusted with part of the army, and given part of the plan to deal with. The commander doesn't deal with those units, he just tells his subordinate what to do with them, and trusts that subordinate, absent orders, to do what seems best. Count Tilly often relied on Pappenheim for this sort of work, and gave him part of the army in most battles to fight. Frederick the Great gave Sedylitz command of the cavalry, and, when he needed cavalry, just told Sedllytz to deal with it.
The thing about all of this is that it's ad hoc. There's no permanent structure to it. If you have a wing commander like Pappenheim, you just say, "These are your guys, this is what I need you to do, I'm going to do this." Even in a more permanent position like Sedlytz's, you're still just giving him whatever cavalry is around. If it's not there, he doesn't get it. However, the Corps d'Armee system makes this whole thing permanent. Each corps is, effectively, a small army, with infantry, artillery and cavalry. It's about 15,000 to 20,000 men in size- easy to deal with for most commanders. (You'll notice that Napoleon gives his better commanders, like Davout, Murat and Massena, much larger corps and often treats them like the old wing commanders- glomming more troops into them as the battle demands, rather than sending independent corps with less capable commanders.) They're trusted with more independent action and authority, within the overall battle plan. This means that the army commander doesn't really need to spend a lot of brain power managing the units in the corps, he just needs to manage the corps, and their coordination. This makes it possible for one commander, with an appropriately sized staff, manage millions of men along an entire front, rather than just 50,000 men in a couple of square miles. Without this system, you can't run industrial sized armies.
Another major impact this era, though, not this battle, would have on those wars is the role this era played in the unification of Germany and the rise of nationalism. Another thing that kept down army sizes before this era was the system of army recruitment. Let's take Austria as an example, since, for this campaign, Charles began using the new system to put together a larger army. Before this campaign, the Austrians relied on their nobility (including, in large part, the Hapsburg family itself) to raise an army. Nobles pledged to raise regiments for the Emperor's service, putting up all the money for the uniforms, gear and so forth, with pay covered by the Emperor. In return, these nobles got to name the officers in the regiment. (That's really a big deal.) The nobles also had to recruit soldiers. Before the Napoleonic era, the pitch focused on a few things: material advantages (Mostly steady pay, mostly steady food and cool clothes), respect, adventure, and the fact that girls like guys in uniform. Sometimes, during war, they might throw in a pitch about duty to your king, or, in a religious war, defense of your religion as a reason for joining up. If they got desperate enough, they would put up a bounty bonus. These recruiters typically targeted peasants- a good third son of a farmer wasn't going to inherit much, might not have good marriage prospects, but was well fed and strong from all the work around the farm- or journeymen artisans who didn't have good prospects for scaring up the capital to open up their own shop and were looking for a change. For officers, duty to the king and the chance for social advancement got plenty of officers for you. If you needed more men, gaols were full of people who just might sign up for a chance to skip a flogging or the noose, but you don't want too many of those guys. The same with landless laborers- they weren't trustworthy, and tended to be smaller because of malnutrition.
To put together a bigger army, you need to tap into more people. Material concerns won't get your middle class into the army- they're fine. And, since they can't advance into the officer's ranks, why would they sign up? A smaller scale of the same issue applies to the laborers in cities and the countryside and the growing working class, too. How do you get them to sign up? You appeal to nationalism. You don't ask them to fight out of duty to the king, that won't sway them. You get them to fight for Austria (Or France, or whatever.) This appeal fills a lot of new regiments that Charles can use, even if they aren't quite professional soldiers.
This appeal to nationalism is pretty strong in the German States, who have to face French occupation. The Confederation of the Rhine and Prussia, particularly outside the nobility, suffer quite a bit from the occupation, and opposition to it serves as a rallying cry against the French. However, to defeat the French takes more than just the small populations of these principalities- it would take every German working together to do it. After the Napoleonic Wars, you see a rise in interest in a unified Germany- an urge that's suppressed by guys like Metternich after the war. However, the roots of eventual German unification are set in this era. (Also Italian unification, for that matter.)