I can't picture a scenario where Minato wins.
Shared vision shuts down any blind spot that could be exploited by Hiraishin. Shinra Tensei or Asura path counter Minato in the event that he gets close. All of Minato's ninjutsu are absorbed.
Frog summons are blown away by Shinra Tensei or Asura paths laser cannons.
In terms of combat, his Kurama avatar can't put down the Cerebrus with physical hits or Rasengan. The only option is launching it away from the battlefield with Bijudama.
Nagato deflects all of Minato's Bijudama back at him with Shinra Tensei, though he can just teleport the deflected Bijudama away.
CT would attract all of the Kunai on the battlefield. It also serves as a counter to a fully charged Bijudama by attracting it & Minato towards the core, far away from Nagato.