I ran for Air Force...and while coaching (new coach since I left) and elevation may differ, the life styles of the service academies are similar.
At Navy or West Point you can look forward too track programs that are well funded and supported and athletes that are highly motivated. These things seem like common sense but a lot of my high school teammates did not have similar experiences in college. Also, doing sports while at an Academy is a great way to have a "life" outside of being Cadet or Midshipman.
The best thing about the service academies is the cost. Money is not an issue so school and running are the focus.
Some drawbacks (big and small)...
1) No red shirting, you get four years to compete, even if you spend a year on the bench.
2) Time management is tough, the academies are designed to stress you out with parades, room inspections, non academic courses and classes, and war games. None of these things are that hard, but between them you also have to find time to do homework, train and potentially do your "military job." Only true task masters will excel at everything, everyone else learns to prioritize.
3) It is not a normal college experience. I never experienced frat parties, binge drinking and general college non sense (I don't really regret that). I would have liked to have dated more, gotten more sleep, and spent less time changing uniforms.
The service academies have great XC teams (Navy and AF had teams make nationals last year) and they are all recognized as great academic schools, whatever the major. But, and this is a big but, unless you want to be an officer in the military (first and fore most, before any "job") they are not worth it.
Once your military service is done, it does not really matter which one you went to, you will likely be just fine. Instead of trying to figure out which school has better post military opportunities, you should be thinking about what you might like to do in the military (and if you did not say infantry right away then stay away from West Point). If the thought of putting on your nation's uniform for 9+ years does not make the 17 year old you giddy, then you are not going to make it through the four years of cynicism and futility that ultimately defines cadet life.