Who would win the fight? Personally I think Alive/Base Minato would win....
And remember that this version of Minato does not not have Kurama inside him....
I'm going with Nagato, Minato and Nagato are both top ninjas and I'm a fan of both. But Nagato is the solo king and never got defeated without plot, while saying that, Minato hype is pretty big. Nagato never shown all 6 elements which he mastered at a young age, The Rinnegan lets him use any jutsu yet he never shown this power, we see it from Juubito while only hearing about it for Nagato. Nagato would be like Obito, fighting with the 6 paths so the share vision and nicely executed attacks will be hard for anyone to fight. I see Nagato winning more than Minato from what we know, We still don't know Minato's full capabilities since we never seen his element jutsus, all of his sealing jutsus, that jutsu he was going to use on Juubi or that jutsu he wanted Naruto to complete.
So as of now, I say Nagato wins more fights than Minato until we see more feats