Depends on what kind of teaching you are talking about. At USC you definately would see more and get to do more than most other places, but at some schools they have more cutting edge stuff that they do. And also how much you get taught at schools matters. Some places, the students are hands on and get's to do a learn more proceedures than other schools (USC would fall here)
As far as residency, if you go to USC, you would get a lot more exotic proceedures and wouldn't just be doing hip replacements all day due to the different patient populations that go to the different schools. So our school is strong in the surgery departments, ER, and stuff like that, but weak in family practice and stuff like that. So really you would need to phrase your question differently and you would get tons of different answers.
As for other hospitals that are like USC's county, University of Chicago has a great one, Tulance (and LSU New Orleans) has Charity, there is one in New York that I forget the school, but we have one of the biggest county facilities in the nation. Of course, we also have a great private program. (diverging a bit) Our county hospital has 700 beds, and our private has 300 with 150 opening in one year (compared to UCLA's total of 500)