But it may depend on what you want.
They are both pretty major referral centers for North Carolina and the Southeast at large.
Duke is a tradition-established training program that is located at a hospital that serves as, perhaps, the premiere academic center of the Southeast. It has very strong departments outside of surgery as well. The program is well-recognized, and almost all of the residents go on to fellowship; and later, many of them attain some sort of leadership position in academics.
UNC is a really strong place also. It might not have the glitz of the Duke name and reputation, but produces brilliant surgeons just the same. It has a major burn center for the state and gets considerably more trauma than Duke. Grads can surely secure fellowships in all of the specialty programs, but the theme is somewhat less "academics" and maybe a little more "community."
In the end it boils down to what you want. Many, many persons preach the "academics" sermon, but in reality it's only a minority of people that end-up as career academic surgeons. Sometimes I feel like you're trained to say "research, research, research," but even most of the surgeons that have labs at Duke are really clinical surgeons and have Ph.D.s running their labs. And I think that is probably prudent. Seldom...actually, never...on the interview trail did I meet an applicant who said "I want to be a general surgeon." Most said that they would like to go into some specialty. But that is most certainly a product of the places at which I interviewed.
If you think you want to be a well-trained general surgeon, and research isn't entirely your cup of tea, UNC would be a great choice. If you like research, or want to increase (however significantly) your chances of going to a premiere fellowship, Duke may be the way to go. Anyhow, I could say so much more on this topic, but I will leave it at that. I don't want anyone to think that I think that either of the programs is superior to the other overall...I just think that they are each better than the other for different reasons. Can't really go wrong either way. Let's see what happens this Saturday evening.