It really depends on the location and what other hospitals are in the area. The line is also very very blurred at many places. Overall, it's probably much better to compare a given program to another. The university program is typically the large academic medical center. In general it's the referral site for the most complex cases (liver and heart transplants, pediatric hearts, very high risk OB, etc.). That's not to say they don't see a lot of general surgical cases, but the patients tend to be skewed towards the sicker end of the spectrum.
Here's where it gets fuzzy, however. Take some Michigan hospitals, as that's where I'm from originally. UMich is the prototypical large academic medical center in Ann Arbor. They do plenty of the big, strange complex cases and are the regional referral centers for the such. Down the road 30 miles you have Henry Ford. Not a university program at all, but a private hospital that happens to do a ton of the weird wacky stuff as well, livers, hearts, etc. All at a non-University based program, so you have to really look at each program individually.
There are some very strong community based programs as well as very weak university based programs. I wouldn't limit your application to only one or the other based on perceived competitiveness, just do your research on here, apply and check them all out on interview days.