Your first question was how competitive are the residencies. That question can be interpreted two different ways. First, are they hard to get. The military roughly parallels the civilian world in terms of which residencies are competitive for selection. A few notable exceptions apply, ER is very hot in the military right now so the military match rate be higher than in the civilian sector. Also, some of the more uncommon subspecialties are underrepresented in the military. For example, I think there is only one neurosurgery slot in all of the military.
I terms of the quality of the residencies, the military claims that they are very good. For evidence they show extremely high step III and specialty board pass rates. Also they note that there residents publish a lot. I get the impression that overall the programs are good with some of them exceptional.
Ed