In my opinion, Minato is the favourite in this fight. Nagato's greatest asset are his gravity manipulation techniques which are effectively countered by Minato's S/T techniques. I don't completely buy the argument the Nagato can Shinra Tensei away all the seals. There is some merit to this argument. However the kunais are in the ground and dislodging them will require firstly knowledge of Hiraishin which Nagato lacks here and secondly, a quite powerful omnidirectional Shinra Tensei which will leave, probably, some after effects on Nagato. People often point out the Shinra Tensei against the frogs as an example of a powerful Shinra Tensei which didn't leave any after effect. However, we have to remember that Shinra Tensei is a gravity manipulation technique and we know that gravity has greater effect on objects with greater mass. Thus, it can be argued that the frogs were blown away because of their great mass.
However, the main argument against Shinra Tensei nullifying is that Minato can leave seal's anywhere he has been. Hence, Minato can just leave the seals on the ground or on trees.
Nagato's CST and CT lose their effectiveness against Minato as we have seen he has seals all over the place. And only one seal is needed to survive to return to the battlefield which is a possibility with seals on the ground and then take advantage of the techniques effects on Nagato.
As for all other abilities of Nagato, Minato has the reflexes and the speed (even in base) to dodge Asura's lasers and missiles. Minato is not getting caught by Nagato which makes Preta, Hell and Human paths' abilities quite ineffective. Animal realm's summons will pose a problem, however, Minato has summons of his own. The frogs can keep cerebrus busy while Minato deals with Nagato. Chameleon's invisibility can be countered by summoning Ni Dai Sennin or using this detection technique.
Having said all of this, it will not be smooth sailing for Minato as the Rinnegan's shared vision will be quite difficult to counter. Shared vision will make it difficult for Minato to get a seal near Minato. However, this is possible with Minato great intellect particularly with no initial knowledge on Hiraishin on Nagato's part. He can use summons to distract Nagato's summons and devise a strategy to place a kunai near Nagato. Oe such strategy can be to start teleporting randomly to different seals and throwing kunai at Nagato to use Shinra Tensei to deflect them as Nagato has no movement speed, however due to Shinra Tensei's cool down, there is a good chance that a kunai can slip through. Furhtermore, Minato can employ Shunshin in conjunction with Hiraishin and then use Food Cart Destroyer on Nagato.
Nagato's gravity manipulation techniques while less effective offensively, will still be a great asset defensively. However, as I stated previously, Minato has the analytical ability to first notice the delay and then come with an effective strategy to counter it. Moreover, Hiraishin is the fastest justsu on the manga, thus even with shared vision Nagato will have trouble reacting to Minato as he does not have reflexes at the level of Minato.
The problem with Nagato is that he isn't much of a planner and mainly relies on raw power to win which is a great drawback against someone like Minato who has excellent analytical abilities and the skills which counter Nagato's most powerful techniques. Minato needs only one kunai in close vicinity of Nagato and this fight is over. Therefore, I am leaning towards Minato in this fight.