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 would say iOS and Android.
Originally they were pretty different in terms of functionality and appearance. Android has improved a lot in terms of the user experience and UI, but also has become more locked down and user hostile. I would say that iOS has actually gotten worse in terms of bugs/reliability, and now Apple is relying on services and ads for new revenue. The user experience has suffered.
If you want a mobile phone/OS that respects user freedoms, agency and privacy, there is no consumer option. Both are filled with spyware/data collection from both the OS vendor and third party apps.
This doesn’t feel like an answer to the question. Sounds like you’re saying that Android and iOS are both now similar, not that one has been victorious over the other.