It's hard to imagine Shanks being inferior to Mihawk, Shanks is literally the complete GOAT of the manga, he is the Roger of this generation, his power is the most monstrous Haki in the world.
For me, who neither loves nor hates Mihawk/Shanks, as well as being a Fan of Kaido, who is stronger than both of them, I don't see Mihawk being superior to Shanks, given what we see in the manga. ( feats )
But anyway, I don't rule out the possibility of Mihawk being more powerful because of his title. At the end of it all, Luffy/BB and Kaido will be the most powerful and there is nothing that Zoro/Mihawk fans can do about that, they are just fighting on the outside