Competitiveness varies from year to year. Likely there is a correlation if HPSP fills that year - the more openings, the lesser percentage of internist selects.
There is a lot of variance as to what 'competitive' consists of. During my med school years, there were a significant portion of folks who definitely wanted Reed, those who definitely wanted BAMC, those who definitely wanted Madigan, or Tripler, even those who wanted El Paso (a smaller lesser known Medcen, but actually has great training potential- quality has really stepped up in past 5-6 years- they had an amazing IM program director. I did not train there, but did serve a few yrs ago as teaching faculty for IM program). I also have colleages who thought their Eisenhower training was excellent.
Training is similar - you could check the board passage rate
My opinion for the MedCens:
Reed - historically solid, some staff personality difficulty per report, has fellows, building is old. Be careful, Reed is slated for closure in the BRAC when it will combine with Bethesda Naval.
BAMC - known solid, excellent building/facilities, friendly folks. Has cards/GI,HemeOnc/PulmCritCare fellows (extra teaching faculty, also good so you can meet the fellowship program directors and they know about your abilities). It is a larger program which has its pluses/minuses.
Tripler - good faculty, excellent waves per report. Folks tend to either love it there, or hate it due to island fever - can't easily go visit family, etc off island.
Madigan - solid faculty, excellent building/facilties. Cloudy for a sig portion of the winter. Close to Seattle. Housing more spendy than you would think.
El Paso - friendly, won in the BRAC- to get 40,000 military and dependents in next few yrs, nicer summer climate than San Antonio, middle of nowhere but you can easily driive to Carlsbad, Roswell, Albequerque, etc. Solid training. The hospital contracts with the VA clinic to provide inpatient care of veterans- excellent folks/great pathology. Lesser competitive than most.
Eisenhower - can't comment accurately, but have not heard anything weak about program.
Synopsis:
1. Any Army IM program will give you solid training.
2. DEFINITELY go and rotate at your first choice (as a MS4 rotating at Madigan, one of the other MS4's tried to call Reed for a phone interview and was told that if he did not rotate there, they would not interview him. And they were not particularly polite about it either.)
3. At least go and visit your second and maybe third choice, check out the facilities, talk with the residents, and interview with the program director. You are planning to invest 3 yrs with them - at least go and see what the place is like. I did that with one of the other medcens as a 4th yr - stayed there for 2 days - spent time with an IM team, met the chief resident, program director, chief of medicine, etc.
4. Go full speed for the program you want. If your grades are somewhat less, so what. Rotate there and impress them with a positive, enthusiastic, hard working ethic. A hardworking solid average doc beats a lazy academic punk.
Sorry, this post ran long, but there are a lot of variables.
Good luck.