Here are some points to consider:
(1) Academically, it's a wash. Depending on which rating system you look at, USNA or USMA will be higher than the other but both are considered excellent. If you go engineering, your education will keep you in good stead with grads from MIT, CalTech, RPI, etc. Any degree from either school will be helpful in life.
(2) If you want to be a ground pounder, both are great options. Almost 25% of USNA grads now go USMC, so choosing that option shouldn't be a problem (although it is NOT guaranteed).
(3) If you think you want to fly, drive ships or subs, think about USNA. If you think you might want air defense, signal corps, medical service corps, intel, think about USMA b/c those aren't realistic options for USNA grads right out of school (some of these might be USMC options).
(4) If you go to USNA, you will spend a lot of time on ships during your 4 years -- at least 2 summer cruises, YP training, sailing training. If that doesn't interest you . . . . If you go to USMA, you'll spend a lot of time doing ground exercises (marching w/packs, land nav, eating MREs, etc.). If that doesn't interest you . . .
(5) As for FBI, CIA, etc -- any military background will be helpful. I had a colleague accepted for CIA Operations (but turned it down b/c he didn't want to spend his first few years in a 3rd world country). Had another accepted for FBI (turned it down for family reasons). Bottom line is that either academy and either service will be equally good.
There is no right or wrong answer as they are both exceptional schools.