And if I take the equalized speed, would it be a stomp?
Technically, Minato is only considered Sub-Rel in terms of combat and movement speed, which MS Sasuke has shown being able to react to. And Sasuke has ways to catch opponents even when he can't tag them conventionally, like with an Enton shield.
Although tbh Minato wins even with equalized speed imo. As Kidkinsey said, spread kunais will make it hard for Sasuke to tag him, and Minato is a much more clear headed and smart fighter than FKS Sasuke. He'll know Amaterasu is trouble and not let it spread too much. It's likely when he spreads the kunai, some will get close to Sasuke (and likely some behind him), and when Sasuke tries to hit him with Amaterasu, Minato will pop up right behind Sasuke and slash his throat off. Since Sasuke has no knowledge of FTG, such a surprise maneuvour will be very effective. If Sasuke pulls up the Susanoo, Minato will enter SM and body it, even if it's the Humanoid version. Even Danzo could pop that open after all.
And if it's the Armored Susanoo, Sasuke won't be able to keep that active long enough to be relevant (although I'm pretty sure Minato could pierce that anyways). Speaking of, the MS strain will be very bad news for Sasuke. If the fight drags on long enough for this to be relevant, Minato will certainly take note of the drawbacks and aim to strike in a moment after Sasuke uses an MS ability and is disoriented.
Also, even in the unlikely event that Amaterasu hits him, couldn't Minato teleport that away? Maybe I'm overestimating FTG a little but I don't really see why he couldn't. It's something he's touching after all.
Even touching it for a split second will hurt a lot, sure, but it's been shown that it takes a while for Amaterasu to start doing serious damage. Karin withstood it for like half a minute after all.
So yeah, while it's possible he can put some pressure on Minato in an equalized speed scenario, I don't really see how he can pull off a win.