I think Mihawk is stronger (until proven otherwise whenever we start seeing feats from him) than any pure swordsman in the series.
When I say pure I mean characters like Rayleigh or Shanks who fight only with a sword (at least we think Shanks does. Rayleigh definitely does).
Characters like Big Mom I'm sure that they're inferior to Mihawk in the art of the sword but they have additional powers that probably make them stronger than Mihawk.
We know Mihawk was Shanks' rival back when Shanks had two hands. Even if Shanks became stronger afterwards, I'm sure Mihawk did too and I predict Shanks' now inferior to Mihawk in a 1vs1 unless he has some unheard of ability or DF. Of course I'm only talking of 1vs1; if they fought as pirates and Shanks had his backup of a crew, which is what makes Yonkous so feared, I don't think Mihawk stands a chance against everyone. It's not like I think he can lowdif Shanks.
Mihawk being as strong as an individual as I think he is doesn't make him superior to Yonkou by his lack of crew and ambition (he certainly used to have ambition in the past to become what he is now. But we now know that he just chills and chases pirates around the world just for entertainment. We also know, from Zeref, that he's the kind of guy who could just chase some random crew around the world for waking him from a nap. We never saw him take anything seriously. And he clearly has no interest in the One Piece or in pirate matters other than killing time).
Another telling of Mihawk's strength probably being very high is that he was the first Shichibukai introduced, yet he's the only one we don't know neither his past nor his current bounty. We even learnt Roger's and all of the Yonkou's before his. I'm sure it will be a big surprise for a guy with no companions.