I think Minato wins, mid-difficulty.
Muu certainly does have an inherent advantage due to his ability to battle at such a long-range, but I honestly don't believe that to be an issue against Minato, someone who is world's most eminent speedster and can Shunshin significantly large distances and scatter kunai throughout the battlefield to evade all of Mu's incoming attacks. I don't think Jinton would be a wise decision given the repercussions it entails for the fighter including chakra consumption which is crucial because lack of chakra hinders reactions, something that's necessary if he wants to evade Minato's speed. Of course, there's also the fact that Jiraiya showed reverence for Minato when he proclaimed that Minato was a ninja of unparalleled strength and we should all know that Jiraiya specializes in close, mid, and long-range combat, so I don't believe Jinton would be enough to turn the tides of the battle, at least, not from a long-range.
I believe the wisest decision to be made is for Muu to take advantage of his invisibility and elite sensing to get within range and even attempt to use Jinton to stagger Minato as he attempted to do against KCM Naruto or if need be, take out all of Minato's clones first which isn't impossible given Muu's reaction speed that enabled him to evade a KCM Naruto clone and that Minato's clones are less reactive than the original. Of course, no matter how sharp and cunning Muu is, I don't believe Minato would fall for such a tactic given that Minato's praised as a genius and a decisive fighter, so even engaging Minato would be dangerous for Muu when Minato can discover the best course of action relatively quickly.
I don't think there's much Muu can do and he'd be susceptible to a bam-flash eventually. I think Minato takes this mid-diff because Minato's not going to dupe an elite sensor as sharp-witted as Muu is with just clones nor is Muu going to force Minato to sudden death as he did with Gengetsu. Minato simply has everything going for him to suggest he'd win here.