Karathen can't replicate anything close to the kind of damage Gojira can take.
On the other hand, it is a bit larger and I don't see him doing much physical damage to it in melee and it is very durable itself.
This Godzilla does not beam spam like heisei or Final wars (which would be a spite match) but he can still nuclear pulse like he did to Muto Prime (see canon tie in comic).
So far every single opponent in the Monsterverse has had the ability to drain Godzilla of radiation except Shinomura which is a pretty big deal. I also think Godzilla wins but I don't wanna sell the Karathen short. It's beastly