Oda often does power scaling via portrayal and matchups. Zoro fights King (YC1) because he is stronger than Sanji who fights Queen (YC2). In terms of portrayal, matchups and feats, Mihawk has never been as impressive as Shanks.
Shanks clashed with Whitebeard, stopped prime Kaido from going to Marineford, stopped an angry, outraged Akainu, made Green Bull, an Admiral shiver with his Conqueror’s Haki from a long distance.
How was Mihawk presented, in contrast? He wanted to “measure his distance” from (old, sick) Whitebeard and was stopped by a Yonko Commander. He clashed inconclusively with a YC3 (Vista), the same guy who got dispatched by Akainu in a second (the same Akainu, who was stopped by Shanks btw).
Another indication is the reaction of the Marines and the World Government to Shanks and Mihawk, respectively. The Gorosei meet with Shanks, Green Bull runs away from him. Mihawk? Is there a single top tier who has EVER been truly impressed by Mihawk? Has he ever been mentioned on a level with the Yonko or Admirals? By anyone? Not really. Not by Kaido, not by the Marines, who sent random guys, not Admirals, to capture him. They failed, but it speaks volumes of his image in the world.
Ironically, Mihawk’s biggest feat is dueling with Shanks (and that’s also his only mention by a top tier, Whitebeard), but that was before Shanks became a Yonko many years ago. For all we know, he was way weaker then, as also indicated by his old bounty.
Aside from that, people only ever talk about Mihawk being the “World’s Strongest Swordsman”, which is telling because he has zero actual feats going for him. It makes no sense to put emphasis on this name/title when we have no idea what it means. For all we know it is simply a title you get from defeating the previous World’s Strongest Swordsman – and as we know, Mihawk refuses to face Shanks. Or it is mostly about swords technique/skills. Not to mention that Shanks seems to be all about Conqueror’s Haki and less about swordsmanship in itself. Similar to how Fujitora or Big Mom use their swords to channel their Devil Fruits.