https://www.reddit.com/r/OnePiece/comments/vfeqxl/_/icvduyg
"Both of those things can be true, and Shanks can still be stronger than Mihawk.
Mihawk could be looking for someone that is stronger than Shanks to challenge him in a sword fight, and while Shanks may lose in a fight if he only used a sword, Shanks may have more up his sleeve than just sword skills that make him stronger than Mihawk overall. Such as some crazy advanced haki that only he can pull off.
Kind of like how Law is a swordsman as well, and if it was just swords, he'd lose to Zoro in a fight, but would win if he used his devil fruit."