Advatages:
Navy: Best base locations, most options for GMO tours.
Army: Best chance of straight through training
AF: Best chance of a civilian deferment for training
Disadvantages:
Navy: Worst chance of avoiding a GMO tour, which can functionally extend your commitment. The Marines (and therefore Navy Med) finds a way to be at war even when the US is at peace.
Army: Worst chance for a civilian deferment. GME largely located in unpleasant locations. Surgery residencies all require a research year.
AF: Worst military GME program, a lot of GMOs that aren't going anywhere, overreliance on deferments means that the odds of getting a particular specialty will vary wildly from year to year, they seem to have the most miserable docs (though this might come from the fact that they tend to attract people trying to game the system and get military money while minimizing military commitments), based on SDN comments docs seem to be more likely to report directly to line officers rather than a medical chain of command, and finally the uniform they give you is an FDA approved form of contraception.
My conclusion: choose the Army or the Navy, avoid the AF.
For FP or EM, does one branch stand above the others?
Not sure about FP, but for EM there's no question that Army has the best programs. They own the only level 1 Trauma center in the military, and they're the only service that has ERs that serve the public. For years the top two military EM programs were also the top two programs in the nation. Navy an AF have nothing close.
Of course you need to keep in mind that in all branches EM is WAY more competitive in the military than in the civilian world.