Post TS, Kakashi implied that his Mangekyo Sharingan should be able to handle Tsukuyomi despite lack of the Kekkei Genkai and judging Itachi's reaction, that may be true. Subsequently, the Rinnegan might be even more sufficient. Though I'm not sure regarding Izanami.
That aside, Itachi's weapons may still be too much for Pain to handle. Amaterasu would destroy most of the pains; only Gakido (absorption) and Tendo (Shinra Tensei) would counter it. Susanoo armed with the Yata Mirror and Totsuka Blade would also be too much. Totsuka could basically just swipe through all the pains, while the Yata Mirror would block any attack.
You could argue about Chibaku Tensei, but what would stop Itachi to immediately target the orb with Amaterasu in its early stage, if not even before the orb started to attract matter in the first place. At this point I'm going ignore the fact that by the end of the series, you could basically outrun Chibaku Tensei..
Nagato vs Itachi would be more interesting. Assuming both are healthy and in their prime, I would probably give it to Itachi as well. Assuming both Tsukuyomi and Amaterasu are useless, Susanoo with Yata Mirror and the Totsuka Blade should still give him the edge. Being overall more skilled and intelligent should help. He is fast, cunning and a master at using feints.
we actually know for a fact Pain can't counter genjutsu with his rinnegan
so how is this an argument
Well, Sound Genjutsu may work different to ocular Genjutsu against someone with Sharingan or Rinnegan. We know that Tayuya's Genjutsu affected both Sasuke and Itachi, hence they had to free themselves by casting a Genjutsu on each other.