Great points u made. But now listen carefully and without being biased. I agree with you bout the genjutsu part that it wud work on him. But remember that Nagato isnt really fighting him, its the Pain and getting 1 path under a genjutsu wont do everything, even if Itachi kills the path he wud be brought back soon. Now for your other points.
1. I already told you bout Tsukyomi and know that its not an easy jutsu to get ppl in and even if he does it will only be on 1 path and the path wud soon be back and it wud cause Itachi a lot of chakra.
2. Yes amatarasu burned him but he wud just use shinra tensei to get it off and even tho he wud be hurt he wont be dead and even if he wud that again will be just 1 path.
3. I admit bout this too but Pain cud use shinra tensei to push back the blade
4. yes it does but Pain wud just use this as a defensive method then
5. Strong attack but it wud not destroy all paths and paths keep coming back and maybe shinra tensei wud push that back as well
6. Yes Itachi is smarter but lacks chakra and the kind of power, Nagato's powers are extreme if you think bout it, what kind of human can fly, destroy villages with one attack, bring ppl back to life, etc.
So you see in the end Itachi's chakra wud run out and wud be killed by Pain, i like Itachi better too but i dont see how he wud beat Pain anymore.