What is Nagato best at? Ninjutsu. What are his weaknesses? Taijutsu and Genjutsu. What does Itachi major in? Taijutsu and Genjutsu. Don't even get me started on Amaterasu.
The majority of Nagato's so called "advantage" over Itachi is Chibaku Tensei, Shinra Tensei, Summons, and the Gedo Mazo. I'll counter all of them.
Chibaku Tensei: When Nagato launched this attack against the trio, it did what it always does: it used its gravitational pull to force them all to fly towards the black orb, along with other debris and projectiles in order to crush them. Itachi escaped it by ordering Naruto and Bee to use their strongest long ranged attack. When they all used it, it created an explosion so colossal that it made me question why they all needed to attack it together.
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The truth is that they didn't need to attack it together. All Itachi needed to do was throw a few extra Yasaka Magatamas and the core would explode, ending its gravitational pull and threat to Itachi. I mean seriously.. the orb is seriously small, smaller than a tennis ball. A few Yasaka Magatamas is more than enough to destroy it.
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Bansho Tennin: As we all know this is the usage of gravity to pull an opponent towards you. This one's quite simple, really. If he uses Bansho Tennin, Itachi can just summon Susano'o and he'll be dragging the Susano'o toward him with Itachi perfectly safe, and when Nagato uses the Preta Path to absorb the Susano'o, Itachi can either leave the Susano'o and resummon it or stab Nagato with the Sakegari Blade, which Nagato
CANNOT absorb due to the fact that it is an ethereal object, something that does not possess chakra and therefore cannot be absorbed by the Preta.
Summons: Itachi already demonstrated what he needed to do to cancel Nagato's visual link. After severing the link, he can simply cast his Genjutsu on the summons so he can use them for his advantage instead of Nagato's. But if he doesn't want to do that, he can take advantage of the visual link and cast Tsukuyomi upon one of the Rinnegan summons, therefore affecting Nagato and exposing his biggest weakness (Genjutsu). So as you see, even if Itachi for some reason doesn't use crows to cast his genjutsu or he doesn't use Shunshin no Jutsu to teleport near his face and cast it, he can exploit the Rinnegan's visual link to still use Genjutsu.
Gedo Mazo: I'm not one of those Itachi fanboys that says Totsuka Blade GG, but taking advantage of the Gedo's massive size should be, well, quite easy. It's not fast, it's not agile, so what's stopping him from piercing it and sealing it with the Totsuka before it launches its attack? That's right: nothing. Even if for some reason Itachi doesn't want to seal it or cannot, Hanzo escaped the soul stealing jutsu by simply teleporting away. Seeing as Itachi's best friend was Shisui the
Teleporter and also happened to be his mentor, I think it's quite true when I say he can just use Shunshin no Jutsu to teleport away from it.
All in all, I don't see this being an easy fight for either of the two. Both are extremely proficient in their own right, and exist in their own leagues, but in the end, I do see Itachi winning this battle.