To me a solid rival is that one team you always have a tough, back and forth battle with. That team is competing for the same prize you are, and you usually have to beat them to get that prize, a.k.a. South Championship, Pac-12 championship etc.
Utah has had more memorable exciting games (with each team winning their share) against USC than against any other opponent since joining the PAC-12. Sad we may not play each other any more for a long time.