I don't belive UT San Antonio is actually VA-based--just maybe VA heavy. UCLA (actually VA Greater Los Angeles Healthcare System, with just a loose UCLA affiliation) is the only program in the country with any actual VA-sponsored residencies (psych and PM&R). To my understanding, other VAs will pay for a number of resident salaries/positions (maybe even a majority), but VAGLAHS is the only one where the VA is actually running the show.
Either way, I didn't interview at UT San Antonio--but it sounded like an interesting program. If I recall it's a categorical program and you actually do 6 months of rehab you intern year (the con being you do six months of IM/intern stuff in your 2nd year, but I think that could actually be beneficial). I believe it also has a Polytrauma center, which is unique to just 5 VAs in the country. A big pro/con is it's in Texas--people tend to feel very strongly about Texas one way or the other.
I did interview at VAGLAHS/UCLA--I liked the program. Very happy residents and easily one of the nicest program directors in the country. It's pretty MSK/pain-heavy (they're up-front about that) so the inpatient training isn't quite as solid as many/most other locations (a common problem with all the CA programs except Stanford). You do rotate at quite a few sites (many are non-VA), and that can (and will) mean a really miserable commute for many rotations... But seriously, the UCLA residents were among the happiest in the country of the places I interviewed.
I actually sought out programs with a strong VA training--you tend to get better amputee and SCI (chronic >acute) training at those locations (mostly because of volume). Obviously places like RIC attract patients from a huge area and will be really strong in those areas as well, but there are a lot of injuries that are more common/unique to veterans that you won't see as often in other programs. Rehab is one thing the VA does really well and is investing in (along with psych). I swear every program with a major VA I interviewed at had a newly-constructed SCI center... I've also yet to meet an unhappy VA PM&R doc--they don't get paid much (relatively speaking), but they have great hours and seem to really enjoy what they do.
I would argue CPRS (VA EMR) is a pro--sure it's ugly (the DOS of the EMR-world), but it's simple and very efficient/user-friendly. It's main purpose is to convey information for the healthcare team--not for billing. I love Epic and all (the other EMR we use), but Epic is really a billing software first (that's how it actually started).
Cons are the VA bureaucracy (it can take a while to get your PIV badge, etc...), ancillary staff are sometimes not as good, (but plenty really take a lot of pride in what they do), silly referrals from the mid-levels since PCP's are often in short supply, the food in the cafeteria is pretty lousy (but sandwiches are pretty comparable to Subway, so they're still decent), some of the infrastructure is pretty old (but also some super new). If you don't like psych or social issues then add that to the con list (I thought they're pros--more to learn). You'll certainly get some malingering--it is the VA.
I think a complex population/multiple comorbidities is a pro for residency training (once again, the whole point is to learn, and patients in general are only getting less healthy), but certainly it can be annoying.
In my experience the average VA patient is much more appreciative and respectful of me and the work I do than those at the community or university hospitals I've rotate through in several states between medical school and residency. VA patients in general are very happy with the VA system (once they get into it--obviously there's a problem with access as seen in the news lately). And taking care of a WWII vet is often one of the most memorable experiences you can have--there aren't many left, but all of the ones I've worked with are as tough as steel and extremely appreciative of everything we do. They just don't make people like they used to...
Still--most rehab patients in general really appreciate what we do for them--there's a reason they come back to visit and say thank you. You can get great training at programs without a VA, but I think a VA is a strong asset to PM&R residency training.