I think the six takes it in all rounds
Nagato vs Hidan? Lol Nagato wins low diff
I thought this said Sage of Six Paths at first, was going to ask how insane you were lmao... But nah I think 6pop takes all rounds. Nagato is too intelligent and would catch on to Hidan's nonsense quickly. He would pick up on his immortal gimmick as well within due time because he is bound to hit him with a lethal technique at some point in all rounds and without Hidan being able to die, he would pick up on it easily I find as his IQ was clearly displayed while edo in the ending war arc. On top of this, Hidan needs blood to perform his rituals. And none of the bodies have any blood. They're dead corpses to have been shown not to have blood when struck by something that would logically cause a human to bleed. So his entire gameplan is destroyed. There's nothing Hidan can logically do her to win much less survive by any fighting means. Nagato beats him in IQ, CQC since Hidan has not real fighting style, its just swinging things recklessly as him not being able to die made him clearly careless and I actually thinks he likes it this way, Nagato outdoes him in sheer amount of techniques and power alone. This is a wash on all fronts.
Two parts here - intelligence and abilities
In intelligence, it seems like Shikamaru barely figured it out with backup (like Izumo and Kotetsu landing the first strike) against Hidan messing around. To me, Nagato being close to Shikamaru is not a problem, but to figure out Hidan who is serious without any of the benefits Shikamaru had requires him to either specialise in intelligence or be very far ahead of Shikamaru in that regard. I need evidence of that. Nagato is the dominant type who does not bother figuring out most opponents but rather just smashing them. Of course this only applies in Round 1.
Then on the side of Hidan, I fail to see why he would mess around with an opponent on his own level. Even if he was someone who jokes around dangerously, it was made clear that he did not respect Shikamaru . . . Against an opponent he actually respects, why would he not fight cautiously, using defensive tactics like playing possum as Tsunade did against reanimated Madara? He actually showcased this against Yugito, recognizing the threat of her attacks and dodging etc.
Overall, I struggle with Nagato being so immensely intelligent while Hidan is so immensely stupid when they both have showings doing the opposite in circumstances such as this.
Then to capabilities, everyone is saying Nagato just does things . . . We have been shown that even a genin like Konohamaru (against Nagato, ironically) can break all trends with fitting circumstances, so the idea of things simply happening without reason fails on me. This especially because Hidan has the showings of being capable even with his own authors practically against him (his arc being rushed).
The other side of this is Hidan being capable of nothing at all. Even if the bodies have no blood, they can still be taken by purely physical attacks.
Going more into his powers, immortality allows him to play a game of endurance (as implied against Yugito) against genuinely anyone. With his speed, separating the paths should be easy considering they suffered that strategy against a Jiraiya Nagato immensely respects and was actively cautious against.
The only other way for Nagato to have it easy here is if he could blitz or overpower Hidan. With Hidan being victorious against a Yugito who is even faster than Killer B in open combat while the paths have a top speed similar to V2 Raikage, Hidan has the advantage there. While I disagree, Kakashi saying that simple knowledge of the paths allows a normal person to counter them makes the idea of them working casually against an immortal faulty.
All this is well represented in the fight against Yugito. In terms of intelligence, Yugito showcased to apply that more than Nagato and yet that was not enough against Hidan and his "gimmick". If anything, she looked confused at the end. In terms of abilities, a monster with swords for claws and living explosives is one of the best combos for taking down Hidan, yet it failed. Accounting for it that she had both those advantages over Nagato and still lost, I struggle to see him having anything close to an easy time.