Interesting. Why would Wolverine have his way with Superman?
I don't think Wolverine would necessarily win...
But if Wolverine surprised Superman, which isn't that hard to do, he could kill him.
If it was a fair and square fight, Superman would win.
The thing is, Superman has to completely avoid Wolverine, because (1) Wolverine, like Cap, would understand how to fold Superman without relying on strength; and (2) A single swipe of the claws would take Superman's head off.
Wolverine has some remarkably useful advantages in this matchup, including:
1) He has no problem whatsoever killing Superman; Wolverine would go all out.
2) Berserker Rage would kick in pretty quick giving him some notable buffs. X-ray/heat vision in this situation is almost useless - Wolverine can survive a nuclear explosion. Wolverine can't be couldn't be knocked out while enraged - again, can survive the shockwave from a nuke - so, he can take a punch. So, Superman couldn't really incapacitate Wolverine in this situation. This pretty much would force Supes hand to go for the kill or bounce.. Knowing Clark Kent, he'd not go for the kill, no matter what.
3) Healing factor... not much Superman can do about this...
4) Reflexes.. Wolverine has much faster reflexes than Superman contrary to what many might think.
5) Adamantium... This plus the healing factor really fucks up Superman's ability to permanently damage Wolverine without going purely godlike, and even then, it'd still be tough.
Even with all these advantages, I still think Superman would win 4 out of 5 times in this matchup from the instant knockout. Superman would find it difficult to use his powers alone to kill Wolverine, and with that it should be said that Wolverine is anything but defenseless... He can win this fight, although he's at a major disadvantage.