I don't have time to quote specifics, but this is in response to those commenting that they think Mihawk is possibly stronger than the Yonkou (minus WB).
So far, whenever a well established character such as Mihawk is shown approaching a crew, the crew themselves don't even try to do anything to him. For example, when Mihawk approaches Shanks crew for the first time (in the manga), the crew quickly runs to Shanks to alert him, they have no intention of fending off Mihawk. Also, when Shanks boards WB's boat, only the commanders even dare to talk to him. This shows that the yonkou crew don't even take part in the battle when characters of such caliber are in the area. to my point, this implies that in regards to Shichibukai and Yonkou, it's the individual shichibukai (as we already know), and the Yonkou pirate captains who face each other.
With this is mind, and considering how separated the yonkou seem to be from each other, if Mihawk (who i actually think is the strongest shichibukai) was able to take out a yonkou captain, i would expect the WG to send him and possibly a marine crew to take out the weakest of the yonkou. of course, there's always the possibility that the other 2 yonkou are your typical "bad" pirates and they are not as honourable as WB and Shanks, and Mihawk knows this and doesn't want to take the change.
anyways, i think this whole debate of who's stronger is like trying to decide who's the best at boxing, tennis, golf etc… in their league, things just aren't b&w, but the speculation of it is great!