I think they were equals when Shanks had two arms and after that Mihawk is uninterested in duelling with someone who is weaker. It goes along with Shanks sacrificing his arm to "bet on the New Era", and that sacrifice is basically him not reaching his full potential (w/ 2 arms).
I think my interpretation is more consistent with their characters. I don't think either Mihawk or Shanks are delusional about their strength. My view is that Mihawk doesn't think a one-armed man can be a swordsman while Shanks thinks that despite his loss of an arm it would still be a contest. Remember Shanks had no problem with the idea of a duel and even kinda threatened Mihawk that he was in a bad mood. Your interpretation has to put Shanks in the position of delusional which is something Oda hasn't portrayed . Mine maintains Mihawk's integrity with the idea of a swordsman, while also maintaining that Shanks isn't being foolish about his chances in a fight.
Regarding his arm, I would love for that to be a storytelling device. I always imagined that Luffy would be told by Beckman or someone that Shanks would have beaten Teach if he had both arms (Assuming he dies to Teach). That would give great narrative weight to Luffy's confrontation with Teach. The problem with this is that an earlier databook said he didn't lose strength as a result of losing his arm.
Roger & Shanks are like Kaidou & Yamato imo, where techniques are being passed down and Oda shows that with Shanks using the same signature move as Roger. And don't forget that Mihawk was also at Roger's execution, he surely doesn't care about the One Piece or being a Yonkou or Pirate King so who knows... maybe Mihawk idolized Roger for his strength as a swordsman?
I don't think that comparison works. I think Oda was telling us with Buggy that Shanks had PK potential. So it isn't like with Yamato where there is no indication that she has Kaido level potential. When they clash she even comments that her Bagua is inferior.
Shanks having PK potential and then using the PK's only named move is telling me narratively that Oda is going the direction of Shanks being as strong as Roger. He even plugged in the hole of him not being PK by having him tell Buggy he wasn't going after the OP.
For me, it's a no brainer that Shanks also uses Roger's swordsmanship, probably also the reason why Mihawk & him duelled a lot. But yea, curious to see what Mihawk's signature move would be that could match Divine Departure.
Yeah it would be amazing to see. The previous vivre card says they sharpened swords against each other which means they used each other to get stronger.
With all the above, I'm still fine if they're equal
As far as we know they are the only top tiers who regularly duelled to the point of them being legendary. They are probably the most skilled combatants we should realistically see. Mihawk for instance couldn't even get tagged off-guard at MF.