^My take on this fight...and it may be hard to believe that I'm not biased when it comes to this, but I'm not. (Nagato is actually one of my favorite characters as well. If he has a fanclub, I'll gladly join it.)
If one thinks Gai vs Madara was a 1v1 fight when he had minor support from Minato, Gaara, and Kakashi...then Itachi vs Nagato needs to be considered a 1v1 fight when he had minor support from Naruto and Bee. Gai and Itachi were the deciding factors in their fights. Naruto and Bee would have died had Itachi not intervened.
As to who's stronger between the 2, obviously Nagato is considerably stronger than Itachi. I would rank him in a top ten list higher than Itachi. But this is what I posted on a thread when someone asked who would win if Itachi were to fight the paths or Nagato.
"Ok. When one says, since Nagato(this is basically Nagato vs Pain, considering that Pain is really just a corpse and Nagato is the one who controls him) is stronger than Itachi in power & therefore would win...that argument doesn't really fly. This isn't a contest on who can destroy a village quicker. This is a 1v1 battle.
Rinnegan is not immune to genjutsu at all. When people state rinnegan>ms, that's simply not true. Zetsu completely discredited this claim when he stated during the Itachi vs Sasuke fight that Itachi planned, "the 3-tomoe has a chance of catching the MS in genjutsu". Rinnegan is a mutation of the sharingan and it is more powerful destructive-wise, but it doesn't have a counter for many of the ms techniques that involve genjutsu. If Itachi wanted to use genjutsu on Pain, it would work and all the paths would be affected due to the shared vision. The reason Jiraiya's genjutsu didn't affect all the paths is because his was an auditory one, but the paths don't share hearing, only vision. That means Itachi has the upper-hand in this respect.
In the databook, it states that Itachi's Yasaka Magatama is as powerful as a bijuu bomb. What did it take for Naruto to get out of Chibaku Tensei in his fight w/ Pain? He just had to transform into the 6-tails and he was out of there, he didn't even need to use a bijuu bomb. When Bee and Naruto asked Itachi what they needed to do against Edo Nagato, Itachi just casually told them. If he really needed their help, don't you think he would have urgently told them right away? Itachi just told them what to do because they were there. It would be bad writing if Kishimoto had Itachi stealing all the spotlight while the main character did nothing. But they overkilled it. Itachi's answer to Chibaku Tensei just being Yasaka Magatama is good enough to stop it. By the way, since the manga states that the Totsuka Blade seals anything it can pierce, could Itachi not just bring out the blade and pierce Chibaku Tensei and seal it away, once he gets close enough to it?
Itachi has an answer to Pain's Chibaku Tensei. Anytime Pain used shinra tensei, he would be looking at his opponent. He could not look at Itachi's eyes, but then Itachi could just summon crows and make them fly in his line of sight and cast a genjutsu on him, like he did towards the beginning of Shippuden. Pain has no answer to any of Itachi's genjutsu, he'll be caught in it. I'm sure that he can break out of Itachi's 3-tomoe genjutsu, but what will he do if he's caught in Tsukiyomi? He cannot do anything. The only one who has a chance at breaking that genjutsu is an Uchiha w/ Sharingan, but even then it lasts only a second. How can one break something that lasts only a second in real life?...you wouldn't even have time to make the handseals necessary to do so. The only time it was broken was when Itachi let Sasuke break it by prolonging it long enough in real life in order to give him a chance to do so during their fight.
If the pains get caught in Itachi's genjutsu, he could just pull out the rods which Nagato uses to control them. If Nagato got caught in Tsukiyomi then it won't end well for him either.
Itachi wins high-diff, Pain loses. "
Note: This person used real-life conditions, so when the characters were alive. Nagato cannot fight himself due to how much the rinnegan drains him and must rely on the paths. Itachi has slight blindness and stamina to worry about, so he should end this as quickly as possible.
Considering that the rinnegan drains Nagato so much, he is more than likely not going to use the same attack that he did to flatten the village, he wouldn't find it ideal for a 1v1. Yata mirror (yes, yes, the hype. However, there is no way to discredit it) deflects most of Nagato's/Pain's attacks (missiles, rods, etc). Amaterasu does work on the summons'. However, some of the paths may attempt shinra tensei and a soul rip to take out Itachi, but when they do that they look at the object they are pulling towards them...not all of Itachi's genjutsu are ocular though. He could point a finger at one, get them to look at some of his crow summons' (both of which caught Naruto in genjutsu when he attempted not to look Itachi in the eyes when they encountered in Shippuden), and a plethora of others...which is why Kabuto decided to completely seal off his vision and rely solely on his senory abilities when fighting Itachi.
Also, for some strange reason, the rinnegan has never been good at seeing through dust or mist clouds. When pain fought Naruto, Naruto was forming hundreds of clones behind a dust cloud with the path looking right in Naruto's direction...he didn't notice a thing until Naruto came at him. And then again, when Itachi stabbed Nagato when the dust from that disabled chibaku tensei was settling. Depending upon location, this could work to Itachi's advantage.
Ok. I guess that's all I have to say about the two. =D