At our school I think it depends on where the attendings work. If they are primarily employed by the VA, but still work with students, they don't have the USF patch but rather the VA patch on their coat. If they are working mainly for the university, they'll have a USF patch on their coat. It depends whether their primary job is through the school or through the affiliating hospital. Of course we don't have a USF hospital, students at USF COM and residents rotate through various community hospitals such as the 2 VA centers in the area, the tampa county hospital, bay front care center, and specialized pediatric hospitals among other sites. So there are different badges and different coats for attendings which are dependent on what affiliating hospital they work at. Even the residents have different badges for different hospitals some times, even if their coat is the same. I noticed this with the neuro residents I shadowed.
I also noticed that most of the male attendings in the VA didn't wear their coats most of the time, but rather chose to dress wearing a formal shirt and slacks, instead. And of the few I've seen, who've worn their coats, one wore the VA coat, while the other had a coat with the school symbol. So I guess it depends on the attending and place of work.