It took me a lot of time to understand why teams and fanbases feel differently about Texas and OU, but I think I discovered part of the answer.
They see OU as a team like them, only better. OU players are chippy, they talk smack, they do little things to piss you off (like lay on your QB for an extra few seconds when the clock is ticking in a 2 minute drill), they gloat, and they have loads of swagger. And they back all of that up with talent and good play. They win. They're like the Ohio State of the Big 12. Other guys may hate that they always win, but they respect them, and would happily imitate them.
They see Texas as wealthy elitists. We play clean and we're good sports, but we look down our noses. If we win, well we were supposed to. If we lose, well we're Texas. I think a lot of fanbases think we get by with money more than anything else. And we're an academic powerhouse to boot. They're happy to beat us because they like to rub our noses in it. They don't respect us when we win, though. We're like Michigan to OU's Ohio State.
Just my thoughts.