Well our Tarheel friend is indeed biased. There's no doubt that UNC has a fine training program. Their Chair is a great guy, a great mentor, they have excellent faculty too. But Duke and UNC have very different missions: Duke has, and will always concentrate on training academic surgeons; UNC is obligated to train surgeons for the community as well as academic surgeons. The number of department chairs and division heads trained under Sabiston at Duke is actually quite astonishing. This attests to Duke's orientation.
If all you care about is whether residents are happy and adequately trained from a technical standpoint, then there really isn't much distinction between the two. In fact, UNC is probably the better choice (aside from the tremendous operative experience [not just volume] Duke residents get). If you want a launchpad for an academic career, Duke, along with other "academic" programs like Hopkins, the Brigham, &c., is the choice.
It's not about "name recognition", it's about what kind of career you want. If you want a nice, cush, community practice, why in the heck would you go to a research-oriented surgery program?--that's just silly.
All that said, here's as objective picture as possible of what Duke provides: First, Duke runs the flat-out best interview process of all surgery programs that I saw. They're organized, there's none of this idle residents wandering in and out and talking among themselves in their scrubs and finagling free food; a representative from each year gives a presentation of what happens in their year, and the Chiefs are responsible for coordinating the process and making sure applicants aren't stuck staring off in space. Each applicant feels that the Program is paying attention to them as an individual, and the number of interviewees is low (as opposed to the Brigham, for example).
Yes, they are traditional...so applicants have to decide whether they like this or not--this is purely personal preference. Their reason for the formal approach is that you know exactly what is expected of you as a trainee. Some people do better in less structured environments.
As for resident camaraderie--actually many residents do socialize with one another outside of the hospital (e.g. meeting at the local trendy bar). It's hard to generalize about such a thing, because dynamics vary from year to year at ANY program.
Yes, interns and JARs wear short coats and white pants, this is probably a bit silly--the only advantage is that people know who they are talking to when they are talking with a surgery resident. Though wearing scrubs outside the OR area is not the mortal sin it used to be; no one wears scrubs in the clinic or when rounding. It's just another feature of the formal nature of the program. Sabiston's original intent was that patients at a training hospital cannot "pick" their doctor, thus it's incumbent on house staff to look as professional as possible.
Decide what you want, and then the distinction between any Duke-type program and UNC-type program is clear.