A more sober Edwardian character than earlier incarnations. By way of comparison, imagine him with William Hartnell's aloof, cultured manner mixed in only somewhat with Jon Pertwee's class.
While looking fairly young and in the prime of his life, on the surface this Doctor might seem old-fashioned. He is a firm believer in fair play and civilised behaviour, quick to lead by example. When agitated, he has a tendency to be pedantic, inadvertently lecturing about whatever scientific or intellectual concept may be relevant at the time.
But the more the Doctor speaks his mind, the more we begin to realise how alien that mind truly is. His scientific knowledge and millennia of experience give this Doctor a different perspective that separates him from the rest of the cosmos. To him, the sky is not blue, but an atmospheric mirror reflecting the colour of ancient waters that he once watched come into being when he was young. He may even get sentimental, but not in a way we might expect: "I've always liked this planet. I'll miss it when it is gone. I wonder what will be here instead..."
This Doctor has a great love of life and the universe, forever reveling in whatever secret they wish to share. Quite literally, the Doctor can be found to be totally absorbed watching grass grow, fascinated at the miracle taking place before him. If ever there was a Doctor who could stand beside Life and call it friend, this one could do it.
Unlike previous incarnations, this Doctor refers to the TARDIS as "the ship" ala William Hartnell. He can often be flippant in the face of evil or pompous authority, picking out the absurdity of such. Some would say that he has something of an ego, though nothing on the scale of Colin Baker's incarnation.