As I ponder Digby's question and the variety of answers it provokes (mine included), I realize that for me part of the answer lies in a range of military history that most historians appear ENTIRELY to miss, contributing to most of the rest of us missing it as well: grand-tactical application.
I think that what I am aiming at is that segment of operations above the battaion and regiment, and below the army division and army corps. How does that sector of anyone's military operate, what were its SOPs, its customs, its norms, its handling?
This segment of military operations is almost invariably missed, in part, because there appears to be so little primary material about it...at least, in English. Moreover, contemporary British thinkers, regulations, and authorities seem hardly to have written on grand-tactics at all! I've just finished reading Luvaas's book of Frederick the Great's writings, and Fritz has little to say about the glue that binds battalions and squadrons into the grand-tactical groupings used on the battlefield...e.g., the brigade. Christopher Duffy, a marvelous historian, doesn't address this level of handling in his recent book on Rossbach and Leuthen, either, nor in his (earlier) book on Fritz's army. Lack of such address makes it harder to form educated judgments about French Revolutionary and Napoleonic practice.
At Rossbach, for instance, the relatively junior Seydlitz is suddenly handed almost the entirety of Prussian cavalry, and told to go get 'em. Rossbach certainly witnessed massed cavalry charges by both sides. But certainly Seydlitz wasn't racing about gathering up squadrons into this new, spur of the moment command, or even regiments. Surely there was some intermediary level that he turned to to group and direct this turning maneuver...but the authorities don't speak of them. Seydlitz must have been on his cell-phone a great deal!
Thus, without penetrating grand-tactical usages in, say the Seven Years War, it certainly is harder to render useful or informed judgments about practices in the French Revolutionary and Napoleonic periods, to distinguish how the practices were different, or similar, or ways in which they evolved...or didn't. For instance, had the Austrians simply fallen out of the habit of massed cavalry usage, or were there other factors at work to inhibit such grand-tactical employment? On the other hand, weren't Coalition forces using huge bodies of cavalry in late 1813 and 1814? In what ways did this usage relate to France's earlier in the war: adoption of French practice, evolution of individual national practices?
For me, the question(s) open up a segment of examination that I think is remarkably neglected, but richly deserves much more attention.
Cheers - Howie