Actually, there's no evidence of Mihawk being stronger than Roger.
Logically there is.
Roger = Swordsman
Mihawk = Swordsman
Mihawk = World's Strongest Swordsman. Therefore Mihawk > Roger.
Mihawk was
famous before the Great Pirate Era even began.
Mihawk also had
legendary duels against Shanks 10-13 years ago.
The term
legendary doesn't come from Buggy, Mrs. Merry Christmas, or Bellamy.
It comes from Whitebeard, the same man who calls Aokiji a
tyke. Aokiji, an individual who is an Admiral.
So, what we learn from this is, someone who is built different (WSM Whitebeard), who has lived through God Valley, a
legendary & taboo War involving Pirates, Marines, and Celestial Dragons
A man who has lived as the rival to the Pirate King himself
A man who led the assault on the Paramount War
Calls Shanks and Mihawk's duels as
legendary
Yeah, Mihawk is definitely stronger than Roger.
Goes back to my original notion. Mihawk, has to compensate for his lack of crew, manpower, and influence, by being a One Man Army. He has to compensate it with his strength. Compared to other Warlord crews who have strong, useful underlings, it makes sense.
But, Oda
can throw a curve ball an make Shanks/Roger all above Mihawk through other unconventional fighting styles, so I am open to that. But from canon we know Roger had influence, power, and a strong crew. Mihawk has himself and only himself, so he has more of a reason to be the strongest.