Not really. He's not even a match at all. To be honest, Wolverine's claws are the sharpest material in the Marvel universe, considering they can cut just about anything. I've seen the Superman not hurt by the adimantium cutting lasers, but there's one problem with that: Adamantium has to be heated to be cut. It makes a sizeable difference. Could Wolverine cut Superman? Not on these forums. Of course, he has the benefit of having a force field (or something to that sort) to protect him from that sort of thing. Still though, there's one problem: How in hell is Superman going to hit him?
http://img118.imageshack.us/img118/6793/fallen44os.jpg
Superman, or anything thrown, would get stopped like a cat running head-first into a brick wall. Here's the whole fight.
http://img108.imagevenue.com/img.php?loc=loc24&image=76154_forg1.jpg
http://img17.imagevenue.com/img.php?loc=loc24&image=0921b_forg2.jpg
http://img143.imagevenue.com/img.php?loc=loc24&image=4c944_forg3.jpg
http://img146.imagevenue.com/img.php?loc=loc24&image=c4355_forg4.jpg
http://img24.imagevenue.com/img.php?loc=loc24&image=e8d48_forg5.jpg
This is what blasts from the Surfer do.
http://img75.imageshack.us/my.php?image=surf0na.jpg
From Genis-Vell
http://img225.imageshack.us/my.php?image=walker31ne.jpg
http://img222.imageshack.us/my.php?image=walker43qy.jpg
Another thing is the case of Mjolnir. IF he were able to pick up the hammer, since this is him from JLA/Avengers, he wouldn't be able to wield it like Thor. Most of it comes from Thor's essence as a god, so Superman would only be able to wield it like Thunderstrike did his mace after being Thor for awhile. He's only gonna have some lightning attacks and so forth. Maybe Teleportation, but not a Kurt Wagner type. He can't utilize the full ability because he's not an Asgardian like Thor, Beta Ray, and Thunderstrike are. Even with these artifacts, he's not going to be able to win this.
Now, if he partnered with Thor, they might be able to do it with some teamwork. Either way, there isn't a way for Superman to really do anything. This is how I've always compared the two:
Superman can defeat Darkseid's avatars, but is nowhere near Darkseid.
Thanos could easily defeat Darkseid's avatars, and would be able to hold his own against Darkseid.
Whew. That was difficult. Good to debate with you Avalon. You're making me think creatively.