I expect Mihawk to respect honor and using a sword and not tricks like King to fight Zoro, that's it.
Oda likes keep things vague ok, but imo this doesn't suggest Mihawk > at best this chapter confirms he's around Shanks' strength, right now being objective is debetable, but looking at Shanks hype and Oda not saying overall stronger I still think Akagami has the edge.