OK , let me start off my rant on which is better... Neither!!
They both have the strong points, and they both have there weak points, but when it comes down to it, its all about WHO is holding that ability, so lets take the only Rinnegan user into action. does anyone know exactly how old he is?? or how old would he be ? is it with Naruto's age? or with Kakashi or who ever, Age counts for experience, and while he may know all the jutsu's Tech's and the works because of the Rinnegan, he is not that old, and i know that much. With age comes experience, and I know about what he has gone through, but like his Faith being lost, it shows that he is willing to do whatever, but to a certain extent. its about his motives and views, which in this case was peace through Brute force. Im sure that if someone like Madara had the Rinnegan, then he would use it to conquer the world, and control it the way he wants to, Nagato is doing the same, but for everlasting peace, and it goes without saying the Madara does and will most likely always have the upper hand.
the sharingan is powerful, Depending on the USER!! Itachi, Madara is about the only ones who would be able to take down The rinnegan, Because they know how to use it its abilities and more. The ems is extremely powerful and i favor it, but in the eyes of someone who can control practically every aspect from gravity, to death, its hard to believe that the Rinnegan would loose. But i believe that Madara would win in a 1vs.1 fight with Nagato. Anyone else with the ems would likely loose because of there motives, and besides, Madara was the brains behind Akatsuki for a reason. As for Itachi, i wont think he would win because he is to kind deep down, and frankly his abilites are extremely good, probably the best i have ever seen, but he just lacks that ability to kill someone, and if you think about it, Itachi never did kill anyone after The Uchiha Massacre.
so in conclusion, its like many of you have already said, It depends on the User and his ideas and motives that shows who will win. Both the Rinnegan and Sharingan, base, ms, or ems, they all are about the same when it comes to the bottom point. but i will say that in a 1 on 1, the sharingan, ems or ms would own the rinnegan, not easely but in the long haul, it would win.