I don’t have any good examples that I know of, but I am very curious. To me though, a rivalry is a rivalry when two or more of people are closely competitive. But is it really a rivalry anymore when someone has more victories over the other? I don’t think so.
Vegeta really goes to great lengths to try and catch up. Goku just makes it look so easy while Vegeta is always taking a beating and getting better, but nowhere near Goku. The guy even lets himself get possessed to try to catch up.