I just finished at Duke and matched in peds (not at Duke - I left NC for personal reasons). It is true that in the past, Duke has had a reputation for being somewhat malignant. However, the attitude of the program has changed a lot in recent years, largely due to the hiring of a new chair, who is fabulous. Compared to other places I interviewed, the call schedule is pretty good and the work load reasonable. Overall the faculty are wonderful and they do a great job teaching, and the residents are a fun bunch. We (the students) all think the peds dept is great, too, and from our class this year, everyone staying in the Triangle chose to stay at Duke (3 peds, 2 med/peds).
I think both programs are solid and I know Duke grads at both that have been happy with their choice. The main stereotypical differences that we hear at Duke are that UNC is better for primary care and that Duke has a more academic focus (at least I think they have more fellowships). Even then, the differences are probably minor, and you can definitely do whatever you want out of either one.