I only interviewed at NJMS so I cannot compare the two, but the consensus is that RWJ is way more respected and competitive. UMDNJ itself is merging with Rutgers so that might change a few things regarding name recognition? If you could only visit one, maybe it would be RWJ just because of recognition alone, but I wouldn't know.
I was very impressed by NJMS and it is actually currently near the top of my ROL if not my #1. The PD is probably the best I've met on the trail. Real down to earth and easy to talk to, and seems to be really interested in pushing the program forward. The residents were pretty happy from what I could gather. A good number of IMGs if you care about that sort of stuff (I am one myself). I don't have this year's fellowship match but the PD's Twitter feed mentions a couple of pretty nice places. Hackensack is kind of far for my taste (~30min from the university hospital?). The biggest con in my book is that it's Newark, and that the neighborhood is pretty bad.
I'm going to put in a plug for NJMS, as I'm a current 4th year student here.
Regarding RWJ, I honestly don't know much about it. I didn't apply there and frankly had no desire to. I think there is a belief amongst many med students around the country that it is more "prestigious" than NJMS, which I think is pure bunk, in my opinion; if anything, the schools are similar but have their own personal strengths. I think part of it just comes from RWJ having better name recognition and possibly that NJMS's IM program takes some Caribbean students and IMGs each year, but these folks are among the best in their respective classes. We take mostly AMG MDs and DOs into the program, and many NJMS students stay in house as residents. Our program director, Dr. Kothari, is fairly new (this is his second or third year running the program) and he's completely revamped it - as said before, changed it to an 8+2 model, drip system for admissions, etc. He is incredibly passionate about the program and responsive to concerns from the residents. He's very well-liked by the students and well-known, as before taking over as PD he was the course director for a sort of transition-to-clinical-years course for the M1s and M2s. Incredibly down to earth guy, very very friendly, and has quite a vision. Given the merger with Rutgers and the money that's going to flow into the program, he intends to really make it a powerhouse.
The clinical training at my program is far stronger IMO as we are a tertiary care referral center located in the middle of Newark; as such we have a huge indigent/uninsured population (as well as a huge immigrant African/Hispanic population) and we see nearly everything, like many inner city programs. We also get people who step off the plane at Newark Liberty airport with all sorts of tropical diseases and medical issues. UH also is known nationally for it's trauma program, so we get a ton of trauma patients, as well as many of its subspecialty surgery programs, so you do meet some very big names in orthopedics, neurosurgery, etc.
Our program itself rotates through three centers - Hackensack UMC, the East Orange VA, and University Hospital in Newark. Hackensack is actually considered one of the best private hospitals in the country and is nationally ranked on many, many levels (not to mention it's gorgeous), and also provides awesome clinical training for residents, particularly in the ICU/CCU; aside from NJMS students they also have a big population of SGU students rotating there so you end up having a few students per team. The VA is much like any other VA and has a strong didactic base. Research opportunities for residents are very easily accessible and available, in pretty much every field from GIM to GI to Cards. Our fellowship match is historically pretty excellent; the toughest field to match is GI, and we still match fairly well for it - this year one of the chiefs matched, and last year another one of the chiefs also matched it. We have an outstanding Heme/Onc match despite not having an in-house H/O program and have sent residents to places such as Columbia and Cornell; for many of our fellowships the residents often stay in house but they also have matched to fairly prestigious ones in NYC and elsewhere. Our Cardiology, interventional, and EP fellowships are very strong and we're known nationally as a top heart failure hospital; they also take many in-house residents (two of the current first year fellows are NJMS program grads).
Re: Newark... it's not the nicest or prettiest city, but it's a fast growing and improving one. The mayor, Cory Booker, is a national hero of sorts and has done a ton to support the city and help it grow, from weeding out corruption to beautification projects etc. The city itself has plenty of nice perks, although the area around the hospital is of course quite dangerous - the Ironbound section of Newark is known for its cuisine, for example, and downtown has a lot of nice bars. The city is less than 20 minutes driving distance/public transport to NYC and about 2.5 hours or so from Philadelphia so there are a ton of things to do in the area. Lots of very nice places around the city to live as well, including Montclair, Bloomfield, Hoboken, Jersey City, Clifton, etc - some residents also choose to live and commute from Manhattan, which is a longer commute but very much doable.
TL;DR, before discounting NJMS as a place to apply, consider that buying into public opinion about a place's "reputation" as compared to another place might be more talk than actual substance. Best of luck to everyone on the interview trail.