Well, alive Nagato is in a wheel chair, so yes. Minato takes him with low dif xd the paths would be far more troublesome in this case.
Edo Nagato was really weakened when he came back to live. We're not sure of his power lvl in this state and how fast he can use his paths, since most he did was summon, and probably 1 or more 2 skills, but cant remember now.
Still, he'd need a great source of power around like a jink to restore his power.
Prime Nagato (the 1 we saw after he absorbed Bee) is a completely different story, that guy is a complete beast. And he can use more than 1 path at the same time, which would make almost impossible for Minato to get an opening to strike.
Conclusion: I understand you're talking about a match up here, and can agree to some points. Also like said above I do think think Minato can take on a weakened version of Nagato... But really don't see him taking a "prime version" of Nagato. I'm sure sure Minato would give him a hard time to catch, but that's it, just a matter of time till "prime" Nagato finishes him off.