I just thought up this topic. I know that W. is invincible and can regerate health, but his only weakness is Admantium bullet to head. Superman is also pretty much invinceble accept for krptonite and a very close nuclearblast to him: he gets most of his energy from the sun. Frank Miller exposed this weakness in Batman VS Superman comic in the 80's
I think it comes down to this... If superman knew Wolverine would battle him, he would punt him or totally obliterate him. If wolverine knew this was going to happen, he would get Kryptonite. If they both knew, I think Superman would defeat him for his speed. If neither knew, I think that Superman would win, because of speed, it would just take a lot longer.
Wolverine needs a torso to regenerate an arm. He also needs a pelvis to regenerate his legs. Wolverine can't regenerate a torso from his arm. I'm sure he needs a head and a torso to regenerate the rest of his body. He couldn't regenerate his brain cells or DNA. Superman doesn't need to regenerate anything. He's invincible. He's super. He's a man. I said regenerate six times. Wazzup?!
Superman is just cheap. A showdown between him and Wolverine (not cheap) would result with him victorious. But Wolverine is about a billion times better character.
Tacky, Superman is beatable if you have kryptonite. Seeing that Wolverine might not have kryptonite with him, I think that he'll lose since Superman is unbeatable.