As a Duke graduate and a Devil's Den moderator, I can assure you that the overwhelming majority of Duke fans hate UNC more than than they hate UConn. For me, I get almost as much joy from a UNC loss as compared to a big Duke win.
Truth be told, there is something to the UConn "took 2 titles right out of [Duke's] hand." The 1999 game was built as a coronation, as only Cincinnati (Great Alaska Shootout) was able to really push Duke until Michigan State did it in the Final Four. But even then, Duke was the favorite, until UConn pulled off what many people believe to be a big upset.
As for 2004, I am not as sure. UConn, to me, was the prohibitive favorite. And we split with Georgia Tech that year, so there were no guarantees of a title. But having a relatively big lead late in the game and being unable to stop Emeka was crushing for me, no doubt. I do not think the title was as much as a "guarantee" in the sense that 1999 was, but it was a devastating loss, no doubt.
So from that perspective, the "hate" for UConn is because of these two losses on the biggest stage.
I agree with your statement about being the defending champions. At times, losing a recruit or a game last year was not as bitter simply because we still had the title of "defending champions."
I do not necessarily see the "hate" with respect to UConn, but I have had the opportunity to meet and hang out or speak on the phone with several Yarders (HuskyNan, EricSanDiego, UCBart, etc.) at various times (including the 2011 Fiesta Bowl). There is certainly a healthy level of competition, but there is also a level of respect for the accomplishments of the respective coaches and programs. I have posted on the Boneyard since 2002 or 2003 (when it was on the Rivals site). Except for some incidents in the early days, I have always been treated with respect as a visitor, and I have, in turn, tried to respond with respect and to demonstrate a level of class in my commentary.
By contrast, I have no such level of respect for UNC.
