When Christopher Eccleston decided to play the ninth Doctor it was more of a gamble than previous actors had taken. The prior Doctor, Paul McGann, had appeared in only a single movie nine years earlier which wasn't a big success, and for the previous Dr Who series you had to go back to Sylvester McCoy, 16 years prior. Perhaps that was the reason Christopher only signed up for a single season, no one knew how successful the new series was going to be. As usual, everyone involved came up with a different reason including the two old standbys, typecasting and overwork.
The new Doctors tend to add something to the character that the other Doctors didn't have. I don't think Christopher did that, unless what he added was taking his job, i.e. saving planet Earth once a week and the universe on a monthly basis, more seriously than his predescessors. He dropped Sylvester McCoy's slapstick bits, traded in the Baker Boys flashy clothes for a black leather jacket and jeans, and lost his cricket bat.
Reminiscent of what William Hartnell, the first Doctor said, Eccleston said, "In all the 20 years I've been acting, I've never enjoyed a response so much as the one I've had from children and I'm carrying that in my heart forever"