They think Shanks is stronger because he's a Yonko. But we don't know who won that dual and we don't know anything about Mihawk except that he's the WSS.
In SBS volume 73:
D: Hey, Oda! In all of these fight scenes, why doesn't anybody go for the men's groins? Doesn't that seem like the quickest path to victory? P.N. Eldest of the Asada Siblings.
O: True, that is a vital area. Just imagine legends among men--Whitebeard, Shanks, Mihawk--staring each other down, bearing their weighty ideals...and trying to whack each other in the balls! IS THAT THE KIND OF MANGA YOU WANT TO READ?!
He includes Mihawk in the same context as Whitebeard and Shanks. He didn't even include Kaido, Big Mom, or the three admirals. The OP community gonna be hit by a storm when Oda introduces Mihawk's flashback and how powerful he is.