If you haven't red or watched a review of chapter 1079.. You are probably better off not reading this.. so stop right here..
However for those that have, let me start off with the obvious.. with whats depicted obviously, it may very well throw off any Shanks vs anyone else besides roger at this point (as roger was the only character to show capabilities relative to what shanks just did), that brings their history of a rivalry in question..
Let me start off with future sight.. which it should've been obvious not only shanks has it, but also most of his crew. He apparently can see much farther than katakuri, (as it makes his prediction about bb all the more foreshadowing), however, when multiple people use future sight it seems to cause an "interference", so even if one can't see farther, they can still affect an outcome, even if only a little, compared to the first future sighting.. However Mihawk's future sight is probably even better.
Mihawk and shanks clearly weren't "fight to the death" rivals, they were more like frenemy "lets get stronger by facing each other" like rivals (not unlike roger and whitebeard), so naturally, shanks never had good reason to use conq haki.. and mihawk (as best as i can tell) hasn't displayed conquerors haki (if im wrong correct me), and because of hawks future sight any situation where he mightve gotten bested because of it, he was able to avoid it. (That's my opinion anyways),
There is the method in which zoro would be able to beat mihawk. Zoro's obs haki isnt great, in fact its kinda terrible. He can't even sense conq. haki in himself. (and he cant navigate a straight line, probably related to that), but if he could overwhelm someone like mihawk with conq. haki, he could counter his future sight