As far as I'm aware, Doomguy can't be killed. Only contained. Bill has no way of truly winning.

Zesty bill

Is getting clapped no homo

The Doomslayer!

I don't think DS has any way of dealing with paradoxical nonexistence or plot manipulation.

Hm....I'll go with Bill Cypher for this one

The Doomslayer

It truly depends, and I'm happy to say a tie if acceptable.