In my opinion, from a top-down perspective on the military structure of the major empires, and based on New Eden's interstellar landscape, certain 'realities' just make the most sense in terms of efficiency of structure. If anything, I think the military structures would largely depend on the kind of technology at their disposal, what they consider a 'fleet' (unit compositions) in space. Now, given that the empires seem to be largely on par with one another technologically, it's not much surprise that they appear on the surface to be similar.
I think where they probably differ significantly is in their military culture and traditions. What is their perspective on war or combat action? What mottos and codes do they stand for in battle? How do they honor their dead?
From their overall culture and the nature of their vessels, you could extrapolate various ideas. For instance, since the Minmatar seem to prefer speed and generally have to make due with little resources, one could infer they prefer recon strike forces and rapid deployment strategies, with an emphasis on avoiding the loss of valuable ships. Or maybe their 'fight to the very end' attitude would lead them to prefer a suicide impact to take as many with them as possible. One could also infer that their generals are the kind of individuals who are resourceful and quick thinkers that can adapt to rapidly changing scenarios, who prefer whittling down superior forces through attrition. (You could just make this shit up..)
I do disagree strongly with the suggestion that slaves would be used in the Imperial
Navy. A professional military, especially as grand and old as the Amarr are going to be a well respected fighting force of experienced servicemen, not a ragtag band of reluctant conscripts. Also, from what I understand, each house has it's own military in addition to the Empress. The implication being that even the Emperor could be overthrown if he/she becomes too unpopular with the existing heads of family. (something Dune-esque there) I'm guessing the military would also be the easiest place for a commoner to be recognized by higher castes within the Amarrian government, and a stepping stool for potential heirs and sons of holder families to build some notoriety. Given the nature of the Amarrian religion and how embedded it is in its society, one could venture a guess they would be rather fervent (one could also say zealous) in their duty, probably akin to the Minmatar's "live free or die" philosophy. In that vein, one could see how their generals would employ in large numbers to intimidate their foes and inspire fear, with an emphasis on brute strength to send their message.
The Caldari, well I like that their Navy is separate from the megacorporations. It seems to be an institution designed to cross boundaries and remind everyone that, while they may have their corporate allegiances, they are all caldari in the end. To that end, I could see many fresh military types starting there, and later moving on into the private sector after their term is up. Maybe, and probably especially with the implementation of the Provist government, joining some branch of the military is probably necessary at a certain age for a certain number of years. Considering how much they push the electronic warfare and technological superior angle, I'm assuming this disruptive technology is utilized to generate confusion amongst enemy fleets, to allow a smaller but more capable fleet to dismantle larger ones. And while their institution may be a lot newer than the Amarrian one, the quality of their officers are probably better because there's not such an emphasis on position/family background to concern with. Of course, the Provist thing may have changed everything...now I'm sure only the most fervent of stooges get promoted while those less than inclined may get the cold shoulder...or worse.
The Federation's democratic government and cultural emphasis on 'enjoying life and its pleasures' seems to line up pretty well with their difficulty in recruiting and keeping a professional military, especially during peacetime. The preference for AI drones and automated systems also makes a lot of sense to minimize casualties and make sure that the local senator doesn't get too much slack for supporting the war with casualty numbers. I also think you'd see a larger population of women in active service ( i know there has been a lot of debate over this subject, but I think the sexes play different roles in different cultures). Also, given the way their culture promotes creativity and freedom of expression, (going out on a limb on this) they might be more inclined to try new fleet maneuvers or gamble on an instinct. But given the state of their new war, I think they'd be playing conservatively and defensively, which is probably a new situation for them as they've mostly been the aggressors.