Weapons: Wolverine has his claws and that’s it. Black Panther also only has his claws. Because of their different types of claws, they have very different fighting styles, but neither has a clear advantage.
Defenses: Wolverine has an adamantium skeleton and nearly unlimited regeneration–in the comics, he regenerated from a drop of blood. Black Panther has a nearly indestructible vibranium suit. Adamantium claws probably couldn’t do much damage to vibranium, and Black Panther’s claws couldn’t do too much damage to Wolverine’s adamantium skeleton.
Skill: Both are very skilled fighters, trained in countless forms of combat. As of yet, Black Panther only has one movie, so he hasn’t had a real chance to prove himself yet. We don’t know the full extent of his skill, but he can definitely rival Wolverine.
Mindset: Wolverine knows no limits when it comes to fighting. Black Panther will stop at nothing to avenge his father. Both are passionate about what they believe. Both “use the dark side”–they use their anger to make them stronger.
Use of surroundings: In the finale of X2: X-Men United Wolverine proves that he can use almost any environment to his advantage. Black Panther has the right stuff, and in future movies there is no doubt he will demonstrate similar ingenuity.
These are two excellently matched heroes, but there is a winner. While neither’s weapons can harm the other, Wolverine is immortal. Black Panther can be killed. Wolverine can keep fighting forever, but eventually Black Panther will die. To top it off, Wolverine has been around for a while, and Black Panther is relatively new and inexperienced. The fight would be long and bloody (as all of Wolverine’s fights are), but eventually Wolverine would come out on top, with brute force if nothing else.