Mihawk and Shanks are equals, as both some of the strongest Top Tiers.
Shanks is a Yonko, plus the protagonist's mentor and someone who is reserved for end game. Mihawk may arguably a bit stronger than Shanks, due to WSS title, with Shanks also being a swordsman. Mihawk is the goal for the second most loved character in the fandom to reach and surpass.
So both Shanks and Mihawk have the same role as benchmarks for Luffy and Zoro to reach and surpass them as Great Pirate (Luffy) and The World's Strongest Swordsman (Zoro). That alone also puts Shanks and Mihawk on similar levels, no matter what.
Shanks vs Mihawk duels are "legendary" in Whitebeard's eyes. For Whitebeard to remember in that regard about the fights between Young Shanks and Young Mihawk, it means that they must have been outrageously strong. And that was many years ago, so obviously now they are even much stronger.
Mihawk being the WSS with Shanks being a swordsman, seems to put Mihawk even above Shanks.
Let's not forget that Mihawk was presented again as WSS in Post Time Skip in both the manga and the databooks, so that means that if he is stronger than Shanks, then it's Current Yonko Shanks that we are talking about.
The terrible argument "Mihawk didn't fight anyone who is noteworthily strong" dies, because Shanks also didn't fight anyone who is noteworthily strong from a lot of time. By Whitebeard's comment, the last great fight for Shanks was... the latest fight against Mihawk.
Mihawk is indeed stated to waiting for an opponent even greater than Shanks to come and challenge him as the WSS.
Guess who that one will be...
Oda's comment on this was "A
gathering of swordsmen! Get cut and it'll hurt!".
All the characters in the picture are swordsmen, by Oda's word. Roger, Rayleigh, Cavendish, Law, Oden, Zoro, Shanks, Mihawk, Shiryu, Hatchan, Kaku, Vista; all of them are swordsmen. It's not my opinion or theory (and I am actually surprised of some of them). It's Oda's.
OPS... I can hear the rustled jimmies.
The delusional haters, the ones "Mihawk is Vista level" "Mihawk is strong but not above YC1 level" ones, should have disappeared after chapters 1035-1036. Because from there we know as a fact that Adv CoC Zoro, meaning Current Zoro, proved to be much stronger than YC1 King. Therefore if Mihawk was YC1 level, or even worse Vista-level, then Zoro would be already much stronger than him, and their future fight would be an onesided stomp. Do someone really think that it's how Oda will have Zoro vs Mihawk to be?
After gaining Advanced Conqueror Haki, Zoro defeated King in three hits (one of them a nameless attack and another a basic Ittoryu attack), without needing to go all out with Ashura (a Santoryu finisher was more than enough), and whatever King tried to do was either dodged, parried, blocked, tanked or overwhelmed. King ended the fight defeated, with his body mutilated and his weapon broken.
King is as more or less as strong as Marco; if one of them is stronger, is by a little bit, they are peers and counterparts as YC1s, the Right Hand Men of their respective Yonko, Kaido and Whitebeard.
Marco is clearly showed and portrayed as much stronger than Vista. Meaning that obviously:
Vista <<< Marco ~ King << Zoro << Mihawk ~ Shanks
To argue against this, then you have to suggest that Zoro is already as strong as Mihawk and Shanks, or even stronger.
I don't think so.
Also. Zoro was portrayed as a King. Meaning that Mihawk, which is Zoro's goal, is the Kings of the Swordsmen. If Zoro is a Conqueror with Advanced Haoshoku Haki, and Mihawk's rival Shanks is as well, you can literally bet your house on Mihawk having the same powers too. It's like it's guaranteed at this point. Zoro, Shanks and Mihawk have to be all similar in strength, that could not be if Zoro and Shanks have Advanced Conqueror while Mihawk doesn't. Obviously he is. He is the King of the Swordsmen, and Zoro will someday reach and surpass him.
And if all of that wasn't enough...
Now an official source (One Piece Magazine) went to kill everything for real. The
Shanks-Mihawk relationship is textually stated to be a rivalry relationship between equals, the way the Roger-Whitebeard was. So as complete equals and peers (or 99.9% peers) in strength. Also they being the benchmarks for Luffy and Zoro to reach and surpass is officially canon.