So the answer to the question is that Wolverine can't kill Superman without giving him arbitrary new abilities or help from outside; and Superman probably can't kill Wolverine but can easily neutralise him permanently.
Of course, both can benefit from scientists giving Wolverine kryptonite claws or Superman adamantium-melting heat vision, but then we're just making stuff up and we can do that ad infinitum.
Of course, both can benefit from scientists giving Wolverine kryptonite claws or Superman adamantium-melting heat vision, but then we're just making stuff up and we can do that ad infinitum.