In terms of CFB, for me, a lot of this has to do with recent history as well. That's why UNC - Duke is so good. Neither of those teams have fallen into tough times in the last decade:
Bama - Auburn
tOSU - Michigan (this hasn't been worth diddly for the last decade because Michigan is bitchmade)
Notre Dame - SC (this rivalry has always seemed anemic to me - doesn't help that we Kiffikins and Weis/Generically Angry White Guy Kelly faced off)
Texas - OU
FSU - Miami (this ain't worth as much anymore since Miami can't pay players anymore)
Before Andy chimes in with Florida - Georgia, this has been even more one-sided than tOSU - Michigan.
In terms of all of college sports, UNC - Duke and Louisville - Kentucky are obviously right up there. Too bad Indiana - Kentucky is no more.
In terms of nastiness, Mizzou - KU fans hate each other for Civil War reasons. It's sort of awkwardly nasty...
Tennessee - Bama seems more regional to me. Nobody north of the Mason-Dixon line seems to get how much those two fan bases hate each other. Also, ever since Foster's fumble at UCLA, Tennessee has stunk.