hmm....you're right on the genjutsu part, but as for the puppets movements, what I mean by "predict" is this. lady chiyo was able to control sakura and dodge the puppets hits, why? because she could see where the puppets were going to attack, I know they are controlled by the user, but even a person without sharingan can try and predict basic movements. when an attack is coming from the left or right you know to duck.sharingan won't predict sasori's or the puppets movements , because they aren't technically human ^^, sasori is almost a full puppet, with no brain, therefore itachi's genjutsu can't affect him, since genjutsu messes with your brain,
genjutsu techniques manipulate the flow of chakra in the victim's brain, Sasori has no brain, no veins , no blood, nothing...Just a heart, the rest is puppet, therefore he can't get affected by genjutsu
Anyways Ot- Itachi beats sasori, , Either with amaterasu, or totsuka sword or something
and since a puppet still have the basic human structure, it's more easy for itachi, it would be harder if it was a whip or something, but the puppets attack from the angles as basically a human would, minus all the kicks and backflips that some ninjas may do. itachi with a mastered sharingan would definitely have more of a chance of reacting that somebody without one. sasuke was even able to see the fast movements of haku once he got his 1st tomoe.