well, the pains were unable to break out of the frog song genjutsu, so obviously the rinnegan can't break out of ALL genjutsu. however, we haven't seen any visual genjutsu performed on rinnegan users so we can't actually judge how good the rinnegan is vs genjutsu. plus the fact that itachi performs genjutsu in every battle he fights but doesn't attempt one on nagato is a bit suspect imo.
personally i think it does grant some kind of protection vs visual genjutsu, the point you make about it being an evolution of the sharingan is sound. reason i think that this evolution things is crap, the rinnegan doesn't build on the sharingan, it's a completely different dojutsu with opposing strengths and weaknesses. sharingan's strengths are seeing through genjutsu, reading movements, seeing the chakra network and copying skills, if the rinnegan has none of that, what the hell of an evolution is it ? :s
Thx and I’m obviously talking about visual genjutsu. You bring up a good point about the key differences between the rinnegan and the sharingan, and it sorta feels like a coincidence (not thought out idea) from Kishi’s side, but that’s what we have to live with right now

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It would make more sense if the byakugan was related to the sharingan,since they both specializes in chakra.
Again your excuse isnt enough. Itachi has used genjutsu in all his 1 vs 1 fights, i dont believe he needed to use tsukuyomi on nagato when bee and naruto were there aswell. I believe since there was help around he instead tried to work as a team instead of him taking on nagato all alone. This is evident in him coming up with a strategy that they could use to stop chibaku tensei. Also evident in him telling naruto that, he has failed in life trying to do everything by himself and giving naruto advise to have faith in his fellow team mates abilities.
If it was strictly nagato vs itachi, i have no doubt in my mind that itachi wouldve used genjutsu.
Anyway i could understand what shikamaru meant by sound genjutsu being the best form. Not because its unbreakable but because it affects quiet a number of people. Evident during the chunnin exam when kabuto used this during the sasuke vs gara fight. Also evident in jiraiya vs 3 pains. But as you saw kakashi, gai, sakura, shikamaru and a whole other characters were able to break out of it. Again it isnt unbreakable, similar to the frogs genjutsu.
Whilst some of the genjutsu used by uchiha are more or less unbreakable.
Your theory sounds more like an excuse than mine. Itachi would not jeopardize all their life’s simply because he wanted to teach Naruto a life lesson (sounds ridicoulous). Itachi did clearly not know about Nagato’s abilities, so he couldn’t predict what was coming, and against such a powerful foe you would think that you would get rid of him by any means necessary (Itachi does not take that kind of chances).As I said earlier Itachi go to move is genjutsu(fact..), and even if it would be smartest not to use it e.g. the Kakashi fight. But it is your opinion, and you have a right to have it, although, it doesn’t seem plausible from where I’m sitting.
Plus it would be a demotion if the rinnegan didn’t possess the same resistance level as the sharingan.
Regarding the sound genjutsu, yes, It is much more beneficial for the reasons you stated above, but you have to remember there are different levels(just like the visuals) and the frog genjutsu was of the highest level(so just like tsukuyomi it would be difficult to break ).