It's always been my understanding that Moriarty is the smarter of the 2 characters, or at best they are equals. However, in the BBC version, I believe Sherlock is smarter by a fair margin, but Moriarty knows this and combats it by taking the offensive. He clearly states that he will kill Sherlock and that he will 'burn him' if he gets in his way. In my opinion, this is a ploy to keep Sherlock from foiling much grander plans.

Moriarty also seems to downplay his intellect by chewing gum, dressing up, general crudeness- to me this is because he knows that he cannot match Sherlock, so instead he throws him for a loop.

Now, does anyone have anything to add? or perhaps to dispute this argument that Moriarty is in fact the smarter of the 2?