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.
I think manga/anime covers mostly one sided rivalry better than a lot of other media. I think it’s that drive for perfection that pushes many characters. One is already shown to be near perfect, and the other is always trying to catch up.
Examples would be Bakugo and Midoria from My Hero Academia. Midoria is by far the most powerful and sees Bakugo as a friend, not a rival, but Bakugo is obsessed to outdo him and keeps pressing himself to find a way to do something Midoria cannot.
I also think of Ippo and Miyata from Hajime no Ippo. There is a bit more 2 sidedness here, but it is mostly Ippo. Miyata sees they are becoming closer in skill, so he leaves the gym to build himself up on his own away from Ippo, and though Ippo beats people that would outclass Miyata, Miyata is still the one Ippo wants to beat since he set him on the start to his success but still was usually one step ahead of where he wanted to be. Miyata wanted to stay that one step ahead, but wasn’t constantly using Ippo to do that after a point, he knew he had to keep looking for greater challenges if he didn’t want to be surpassed.