There is a difference between a rivalry and archenemy tho, and then another difference with just straight up enmity.
For example, imo:
Ken and Ryu = rivals, even though they are friends and on the same side. So friendly rivals. But theyre rivals cause they both come from the same school of martial arts and both are finding their own way to be the GOAT.
Now take Ryu and Akuma, or Ryu and Sagat. Also rivals, but definitely not friendly. But they're rivals cause of similar skill set even though one is Muay Thai and the other is Dark Hado. That being said...
Wolverine and Cyclops to me aren't really anything but romantic rivals. Wolverines's rival is Sabretooth, and probably Deadpool. Similar skill set and in direct opposition.
Same with Batman, I don't see the Joker as his rival, more like his archenemy. To me Batman's rival has to be either Deathstroke or Bane, possibly Ra's Al Ghul as well.
A rivals gotta be somebody who is almost like your mirror image, or else it's just a nemesis. And from that list imo I'm going with Goku and Vegeta, they actively have gone through all the stages of rivalry from openly hostile, to begrudgingly allies, to open hostility again, to a peace treaty (for now) but still trying to one up each other. Not even Naruto and Sasuke are that deep in the rivalry game
Not mad at Leo and Raph tho, or Spiderman and Venom.