The rinnegans of Nagato and Madara
Nagatos' rinnegan was gifted to him.Tobi stated that he's the one who guided Yahiko to find Akatsuki and he's the one who gave Nagato the rinnegan,when fighting Konan.He said that he's just taking what is rightfully his.(chapter:509 page:4)So we can assume that Nagatos' rinnegan wasn't originally his.He might have been chosen because he is an Uzumaki with a huge chakra reserve and stamina.Despite that Nagato was able to control the six paths and well as perform huge techniques like 'Chibaku Tensei'.
Madara too has a rinnegan.Madaras' rinnegan was originally awakened by him.We saw him perform a unique technique.He brought meteors from space.We haven't seen Nagato performing that jutsu.If he can't perform it it might be because he's not from the bloodline or the jutsu is out of his reach.
However the story behind them might be this.
At the time Madara awakened his rinnegan he was near his death(injuries from the battle at the final valley or age).He was too weak to operate.So he takes Tobi (whom we don't know actually :shrug
as his accomplice.They plan the 'Project Tsuki no Me'.Madara chooses Nagato to pass his rinnegan in hope to return when the time is right and their plan is on the move.They planned to use Nagato and rinnegan to revive Madara again.(proof that Madara thought that he is revived by Nagato:chapter:559 page:2).Tob is the person appointed to carry on the plan after Madaras' death.Then Madara dies.When he's revived by 'Edo Tensei',he is disappointed.But hes' reanimation is better than his 'prime'.So i think this may be the story between Madara and Nagato and the starting point of project 'Tsuki no Me'.And do you think there's a difference in abilities in their rinnegans because of the above reasons?
(Theory Only)
Feel free to express your opinion! 
