User blog comment:AYET/Mihawk - to the NW and back.../@comment-3986064-20120220151506/@comment-3425840-20120222005907

He never had any on screen battle with a Logia so we can not surely say that he can fight on par with them. He spotted Luffy but that could be owing to his awesome eyes known as hawk eyes. His sword is a highest grade sword so it must be pretty resilient to the point when it can stand up to even Shanks' haki. (Although I do think that Mihawk has haki, my point is that it is still pure speculation without valid backings)