Okay, time to end the conversation. I do agree with FFA partially, though the topic is way off course.
The question is in this topic, not Shank's primary fighting style, or what makes anyone better, worse, or different than anyone else. The question posted was; is Mihawk the stronger swordsman. To that, it should be agreed 100% that yes, Mihawk is the strongest swordsman in the world. (Its his TITLE).
As far as One Piece and the rest of the Odaverse, we're not sure if One Piece even EXISTS. "Sure, you can have it, go find it." I honestly believe that One Piece doesn't exist, its rather the achievement of a dream. The reason Roger is credited for One Piece is because he was publicly executed.
Mihawk is the best swordsman, period. Shanks probably uses a variety of fighting techniques outside his sword. This is evidenced by his gameplay in One Piece Grand Battle series of games (Grand Battle 3, Rush, and Adventure). As far as who's stronger, Mihawk is; but he's also slower and has less variety in his techniques than Shanks.
Shichbukai are on different levels on their OWN, Crocodile with 81 MB, Doflamingo with 340 MB, its obvious who's stronger due to their reputation. Also in the Odaverse, he defies modern Fight-Anime's by avoiding the subject of "Power" as a source for how strong characters are. Character's traits are what determine the outcome of most battles.
According to the Marines, their main opposition is within the Yonkou, as they are the strongest pirate FORCES in the world. The Yonkou are probably very powerful themselves, and it remains to be seen what level they are truely on. My guess is that the Yonkou leaders are roughly as strong as a Shichibukai privateer; their only real advantage comes from their crews.
Currently, the Yonkou have an advantage, due to a Shichibukai position being lost. Imagine losing a single brick in a wall? Even a tiny hole can be inspiration for the pirate forces to assemble and break through the hole.