Renningon>byakugan>sharingon----->thats how kishi establish it in his manga.
second Rennigon is the most strongest eye's in the series i am sure it is can break out of genjutsu in a hard beat-
The Rinnegan is characterised by a ripple-like pattern over the eyeballs, with a light purple iris and sclera. It is said to be the most powerful of Great Three Dōjutsu Daisan Dōjutsu; Literally meaning "Great Three Eye Techniques"). It was admired as being able to bring forth all ninjutsu. The holder of these eyes can completely master all five basic nature transformations that form the basis of ninjutsu. It was said that in times when the world is in disorder, a person is sent down from the heavens to become either a "God of Creation" who will calm the world, or a "Destroyer" who reduce everything to nothing.[1] It also allows the user to use all of the six paths techniques as well the seventh path - that is "beyond life and death".[2]
The Six Paths of Pain were all reanimated corpses that Nagato gave the Rinnegan to through some unknown means. By doing so, Nagato could see each individual body's field of vision, coordinating the bodies with extremely precise planning. The animals summoned by the Animal Path also possessed the Rinnegan, so Nagato controlled and also shared a field of vision with them and the King of Hell.[3] On its own, the Rinnegan allows the user to see chakra, including otherwise hidden barriers. It can also decipher more of the Sage of the Six Paths' tablet than the Sharingan and the Mangekyō Sharingan are able to.