You'd get the best answer on this question from someone who has completed a military residency. But, here's some quick information I can offer. Other than receiving a bimonthly paycheck, reimbursements for books and equipment, summer training and no debt, its pretty much the same med school experience that everyone else has.
As for post-grad residencies, its pretty much like any other residency, except you get payed a little more and you wear a uniform. The army has the most residency slots in the most specialities amongst the four services, but you can specialize in anything you want in any service.
The largest difference between military and civilian medical careers does not really begin until after residency. For a small taste of how things differ...well, just watch CNN, MSNBC or Fox News these days. Post-resident military doctors generally get payed less than their civilian counterparts, but they pay no malpractice insurance, and have no debt. Also, as practicing physicians, they receive additional pay according to their specialty, so they end up with a much larger salary than other officers of the same rank.
Here's what it boils down to: with a military scholarship, you'll relieve yourself of most of your financial burdens, and you're probably no more or less likely to enter your desired specialty than you would be in the civilian world. The residency training in the military is probably as good as, if not better, than any at a comparable civilian hospital. However, once you finish residency, realize that a military career involves frequent moves (sometimes to areas of the country that you might not like), and even more frequent deployments. If you want more information, call a service health care recruiter. Although in a sense they are "salesmen", if you ask them a straight question, they'll tell you the truth. Good luck.