I think that last weeks chapter proves Mihawk > Doffy because law stated that Kaido will mop the floor with him and Mihawk casually clashed with Shanks and refuses to do so now since he has on arm Also, Kaido is the world's strongest Creature. Creatures include birds, dogs, humans etc. So Kaidou is stronger then any individual going by the manga statement
In the Marineford arc we found out that Shanks persued Kaido not to attack WB, and Shanks reached Marineford without a scratch. This implies that Shanks is at the very minimum as strong as Kaidou if not stronger.
So bottom line... Mihawk strongest Warlord of the sea.