They are both genius, but I think Sheldon is more intelligent.

To be hounest, I can't really say that I agree. Though Sheldon is intelligent, so is Artemis, and he excells at skills that are far behond Sheldon's reach, for example when he portrayed the young, somewhat more modern and normal boy in the beginning of The Eternity Code, this is something I cannot see Sheldon being able to do, as he lacks the knowledge one needs to take on a role like that...

Though he may not have an eidetic memory, Artemis was still able to decode the book of the People, pretty much on his own, and he managed to outsmart each and every one of them, rarely beoing outsmarted himself, as Sheldon is easily tricked by Howard (and his card trick), Leonard's gilfriend Dr. Stephanie Barnett (telling him that he had become sick and could no longer talk), and even Penny, who he sees as far less intelligent, tends to be ably to fool him with ease.

Artemis on the other hand, has still to loose completly to someone, and he tends to drive them mad while getting back at them for trying to fool him. ^^

@HappyLilBadger - I guess you do have a point there.
I'll change my pick.

Both are equally intelligent, but I chose Artemis because he was losing. :P