the sage was the epitome or at the peak of his godly powers when he was BOTH a bearer of the rinnegan and jinchuuriki of the jyuubi.
his power was then split into his two sons, into the power of doujutsu(which has produced some deadly abilities), and the power of having a body capable of housing a bijuu(which is raw power in its own right)
his younger son was probably able to easily house the kyuubi, not saying he did, just saying his body was probably able to with little problem if need be; maybe his body would be able to withstand even the jyuubi, can't say for sure. this is the power that was inherited by the younger son, NOT any eye powers.
people shouldn;t say that the rinnegan was split between the two sons because it wasn't. the sage's eye powers went strictly to his elder son.
my question is why did the rinnegan change when passed down to the elder son, the elder son has a doujutsu which isn't mention by name, yet has a unique pattern/design not seen anywhere else, we have no idea what his eyes were capable of. i hope that sasuke when reaching the peak of the power of his lineage gains these mysterious eyes so that we can learn about them and see what they were about when it came to battle. were they able to externally tame the jyuubi like the sharingan can externally tame the kyuubi??? who really knows but kishi.
anyways, the eye powers of the sage went directly to his elder son and only his elder son, while the power of his body aka the ability to be a jinchuuriki went to the younger son.
we know what happens when someone who does not have the body of an uchiha tries to attain the sharingan, flaws eventually manifest. while the body of an uchiha can easily bear such power. so perhaps it takes a specific body, even stronger than the body of an uchiha, to retain the rinnegan with no problem, so perhaps the eyes of the elder son were "limited" for this reason alone, he didn't have the body capable of holding such power since his younger brother inherited the body not him. regardless, the younger son didn't gain the power of his fathers eyes in any way whatsoever.
SO, perhaps the full power of the rinnegan was locked away in the elder sons' eyes and all his descendants which would explain the possibility of a sharingan or EMS somehow turning into the rinnegan, possibly with some help from the genes of the younger sons lineage.. the genes are capable of unlocking this dormant power within the eyes. so, madara really did somehow transplant his eyes into nagato's eye sockets knowing he was a descendant of the younger son, so unlock the dormant rinnegan power within madara's eyes..
hmmmm, so many question i hope kishin clarifies for us.