I think "when [you were] a kid" is the key point there, MrNubbz.
Imagine TOSU vs. Michigan as an OOC rivalry that was just as important as it always has been, but more hateful and ugly, and played at a neutral site in the midst of the State Fair of Ohio, in Cleveland. That would be Oklahoma vs. Texas during the Big 8 era.
OU-Texas was just as important as OU-Nebraska, but very different.
I can't speak for the Horns, of course. But my guess is that Arkansas was their 3rd-most important rival at the time, with OU and Texas A&M taking the two top spots.