Was just thinking this through the other day...and what each empire military has as its primary doctrine, as well as the individual day-to-day culture of each one (we get a lot of insight into American military culture from movies and media, but I doubt this is universal across all four militaries). I've added a 'RL comparison' bit, which is my own purely personal opinion as to how you may compare and view each military and how it behaves. It's a very small detail, but I doubt you can just pull out the four militaries from Call of Duty Modern Warfare and use that, given the distinct developments and rise of them (especially the Amarr)...the examples I provided are designed to add flavour, especially the Amarr one.
So, some examples...
Gallente - "Minimal loss of life"
Given the extensive use of drones, though this has changed recently, I think this is the most accurate one I can think up of, considering a democracy is generally anti-war, and large casaulties are very often frowned upon. Since most people paint the Gallente as a 'Western' faction, then one would compare our current day military which very much reluctant to avoid unnecessary deaths.
RL comparisons - Mixture of US and UK militaries (ie. former always trying to be on top of the game even in the lack of a cohesive conventional military threat, but the latter always suffering from budget and political downsizing, due to the lack of a cohesive conventional military threat)
Caldari - "Total defence"
From a comment by Mens Reppola about how the Caldari Navy is not designed to extended offensive actions, but to protect the State, as well as the mention that the Citadel is "the most fortified region of the cluster". Their Navy is designed to defeat any other in the world, but in a practical application, I think this is foremost designed to protect the "small, fortress nation" that is the State, as the Caldari aren't really into 'power projection' unlike the Empire or Federation. Also some fleeting mention of Caldari worlds having the most planetary defence too or some such, and how the Caldari Army is the weakest armed force in the State, playing to the idea that they are not designed to be conquerors.
RL comparisons - Israel, Japan, Singapore, Taiwan (ie. "Small yet advanced")
Amarr - "Unquestionable victory"
Quite a fun one...piling in as many units as possible, and expecting victory through pure size, regardless of actual quality of each unit. In addition, I believe cowardice and retreat are punished by slavery or execution, ie. you MUST never retreat, and must always fight. This is somewhat interesting, and is kind of related to the Japanese Bushido thing no? Also, what does this say of individual tactics and strategy? Are the Amarr military the "least trained" (considering use of slaves as well) in modern warfare compared to the others, if all they are relying on is numbers? This is what I think makes it the most interesting, a sci-fi military centred around pure attack, and not following current modern tactics employed by RL militaries.
RL comparisons - Russia (especially WW2 era)? Probably the least similar to any current existing military
Though there's stuff for the Minmatar, I can't really think of a name for their doctrine, or any RL examples, but I'll leave that to others...feel free to question, strike down and provide alternatives for the stuff I've provided. I love flavour that defines each of the New Eden factions as their own entity so \o/