Very nice summary. What I was looking for. Is less flexibility a bad thing? Would it maybe mean that you're more likely to match into a residency that's within that flexibility?
it means the government owns you for 4 to untold years depending on how you enter, and many specialities are near impossible to go into (for example a friend of a friend who wanted to do Navy and be a plastic surgeon had to do two general medicine residency years, or whatever the military wants to call them, waiting for a plastics residency spot that they offered her to open, as they only train a very limited number of plastic surgeons).
you might want to go into the military medicine forum to find out how much "traveling" you will do... I suspect, especially in the army, it may be less than you think. most stations (for other MOS) are at least two years, and even when we were heavily in Iraq and Afghanistan I'm not sure a year plus in country really counts much as "traveling."
that said, there are definitely some benefits to military medicine (personally i wouldn't consider no student debt, if taking the HSPS, as one like others might as the lower pay in the military counter act this "benefit" and you can always join later and serve 10 years and have anything you haven't finished paying off disappear).
personally, i would only probably do it if i had already served in the military, particularly in a special operations force (Ranger or SF tabbed, SEAL or PJ) with the hope of getting assigned to one of those groups as a physician (there is an old thread about this in the military med forum)...