This is a text book example of a battle for Attrition. Logan can't kill Kharn as he would simply vanish to the warp only to return later. I also don't believe Gorechild (Kharns Axe) would do anything against comic-Adamantium.

Overall Kharn absolutely curb stomps Logan in QCQ, Both would never need to stop fighting due to their individual powers. If Logan can get in close and use those claws, then he can surely leave a mark.