Ok, I heard and read about that the original Sheogorath gave his powers to the player character on Oblivion (got the game just resently so I've havn't went to the SI yet,anyway),but on Skyrim you meet Sheogorath in the dead mind of Pelagius. Okay here the maddness topic start now.
1. O. Sheogorath he going to take your eyes out on Oblivion, and some people think that Skyrim Sheogorath is blind. Well, for me and probably others, thinks he is not blind but instead have glowing white eyes.
2. This about Skyrim Sheogorath is the player from Oblivion. Okay some people might think this is crazy what about to type down but I type it anyway, I think Skyrim Sheogorath is the original.
For one I read somewhere that at the end of SI, when Jyggalag name you Sheogorath he also said that you can't be a Daedric Prince as well what I heard/read, but on Skyrim he said this "If not... Then call me Sheogorath, Daedric Prince of Madness. Charmed.". And second, he's mad yes? If he can enter the mind of a dead person he probably can enter the of living people also on Skyrim he sound he did before when he ask you is it your first time, what I'm getting at that he probably enter the O. player mind and seen his/hers throughts & he merge them with his(If the player did the main quest before this.).
Alternative: If the player did SI first instead the main quest, then that Sheogorath is in your mind and seeing what you doing in the M.Q.so that he said all that on Skyrim.
Another alt.: Sheogorath spirit/soul took over the dead body of the player, one the player is mortal so you he/she going to past away between Oblivion and Skyrim and two for Sheogorath said you remind of himself you may a desentent to the player on Oblivion(well could be, just the second part just out of random).