It's hard to pinpoint just one moment when everyone realized last season was spiraling downward, but if you were going to rank a bunch of them, the Texas game would be in the Top Five. The Heels already had losses to Syracuse and Kentucky, both due to incredibly lopsided runs by their opponents, and came into Jerry Jones' new stadium trying to find their way. Instead they were embarrassingly outrebounded 54 to 37, were victims to a 23-7 run in the first half, and gave up 100 points in regulation for the first time in Roy Willimas' tenure. It was not a good day.
The good news is, most of the players who had their way with Carolina have moved on; of the four 20+ point scorers from that game, only guard J'Covan Brown remains. Also gone is that strong rebounding presence, as the Longhorns now rely on 6'7" Jordan Hamilton (who prefers the perimeter) and 6'6" Gary Johnson for boards. Southern Cal outrebounded and pushed Texas around inside, in no small part because of Alex Stepheson, in their 17 point win a few weeks ago. Provided the UNC bigs don't have a second lapse like they did against Long Beach State, they should be able to dominate similarly.
Defensively, Texas relies on good shot defense and hasn't done much to generate turnovers. The latter is especially a good thing for UNC, as they still cough the ball up enough on their own. Don't expect another hot shooting night for the Heels, but working the ball inside to Tyler Zeller and John Henson for high percentage shots should pay dividends. Texas will run with Carolina, as last season showed, but don't have the combination of quickness in their frontcourt to stop UNC if it comes to that. If they can force Carolina into a half court offense and make the Heels shot over them, though, it could get dicey.
Texas is a dangerous offensive team. They haven't been shooting the three very much at all – look to Hamilton and freshman Cory Joseph to have the most success there. They'll mostly try to get their points in transition, which provided they don't come off steals, Carolina should be able to defend. A lot of people underestimate the speed of Henson and Zeller particularly. The other key is that Texas is not very deep at all, and can be drawn into fouling. The Heels' frontcourt is, of course, great at drawing fouls and will try to use it in the same manner they did against Kentucky. Rick Barnes has had to play four-on-five against Carolina once before, back in his Clemson days, so may be on the lookout for such a thing, but his teams play physically, and getting them out of that game can only help UNC.
This is a very winnable game for Carolina, on a national stage. Texas squeaked by Illinois early in the season, but they don't mach up with UNC very well; a win here going into the slow games of the holidays will do a lot towards building momentum for a strong start to the conference season. And revenge for last year wouldn't hurt, either.