One invaded a country and forced himself on the throne. The other one is the queen of an island of fodders. It's like saying Mihawk trashed the baboons and rules over an island. Mihawk has greater ambition than Hancock and Katakuri, by far. He aims at being the strongest, to stand at the top. CoC is ambition. It is used interchangeably in the manga.
Doffy and Hancock are both leaders and their underlings are devoted to them ... Mihawk don't have any of this