I'm a Navy CA-1. I don't know anything about Army programs, other than that the one at Walter Reed is combined with the Navy Bethesda program (ie, National Capital Consortium).
I'd avoid Walter Reed like the plague. That place ought to be knocked over, no two bricks left atop one another, the ground sown with salt. I'm equivocal as to whether or not a 30 foot wall should be built around the site and sprinkled with radioactive cobalt. Approximately 93.75% of my unhappy USUHS medical student memories involve Walter Reed in some fashion.
Military residencies, in general, have good didactics and produce impressive board scores; there's usually a very comfortable team/supportive atmosphere between the residents, ie competition with peers is minimal. All military programs (anesthesia or not) typically suffer from the same set of shortcomings though - overall lack of acuity, fewer big cases, a lot less trauma, almost no HIV, generally weaker/younger support staff with high turnover, and high attending turnover/deployments. I think most will agree that military anesthesia GME hasn't suffered as much as some other military GME programs in recent years. I'd be very afraid of entering primary care in the military these days.
militarymd is an ex-Navy anesthesiologist who trained at Bethesda and (I think) served out most or all of his time at Portsmouth; I'm sure he'll pop into this thread at some point. Hopefully he or someone else can give you more Army-specific info.