I think that Tennant and Smith play very different characters. Tennant was very energetic and animated, always moving and talking really quickly with all those funny asides.
Smith plays a relatively quiet person. He's a lot more reserved, and kind of seems depressed most of the time. He's like Dr. Emo. He doesn't crack as many jokes, as well. The biggest thing, however, is that he gives in to the zero sum games that he has to sometimes play. For example, in the episode where
He had to decide whether to let the giant whale powering the city suffer. He actually picked a choice that wasn't the best one. Tennant's doctor would never have done that, he always finds choice C. Yes, I know that the episode was where the new companion had to prove her worth, but still...
