Oh Minato vs Itachi, throws me back
Anyway as far as their battle is concerned, I think knowledge is important. It all comes down to the genjutsu vs ftg debate, but knowledge dictates how much easier either can take advantage of this
However few things to note. With his speed, hax(teleportation, ftg barrier, sealing techniques), sensory ability, things like Amaterasu or Susanoo are completely useless, and since Minato is a natural sensor, capable of clone usage, with perfect chakra control it makes it extremely hard for Itachi to manage a genjutsu since not only clones counter genjutsu, but he can sense chakra flow to detect any genjutsu use, and with perfect chakra control can even break any genjutsu outside of tsukiyomi
A simple throw of ftg kunais and Minato already controls the battlefield environment, forcing Itachi on the defensive(Susanoo) to potential prevent fast/blindside attacks, pushing him under pressure(potentially attacked at any moment, Susanoo chakra use, drawbacks) without Minato having to do much
Furthermore, he only needs one touch to end the fight due to permanent markings, which given his speed, intellect and potential distractions(ftg kunais, clones, ... ) is easier to happen.
And that's discounting things like ftg swap(which might allow him to get rid of Susanoo), ftg lvl 3 which we never got to see, sealing techniques, SM with summons(although not really in character for him, but amphibian technique might theoretically allow him to counter his SM duration issue)
In terms of portrayal as well, Itachi considered Obito(who he thought was Madara) as his superior mentor who needed the EMS to be surpassed, when Minato could beat him fast even while lacking knowledge, and being under pressure(Kushina/his newborn son, the Kyubi(the strongest biju), the village). Later in the war arc, he even got KCM which only happens if you manage to best your biju, and in the recent one shot, his potential was even compared to Hashirama's(god of shinobi), although he died too early to realize it
All to say that Minato is overall the superior fighter
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As for the Mihawk vs Shanks debate, Shanks has always been portrayed as a swordsman and Mihawk is the strongest swordsman.
But it's implied they never settled before Shanks lost his arm, and both grew stronger since then, with Oda always leaving it ambiguous.
So while there is more reason to view Mihawk as stronger, I'd not be surprised if Oda viewed them as equals. It might also depend on how Oda will develop the black blade stuff