It's hardly surprising that 'The Christmas Invasion' was light on The Doctor, since Rose was the star of the two series that she appeared in. Those two series were totally about her: being stuck in life, finding confidence and purpose, etc. It was only when The Doctor was on his own during The Christmas Bride that he emerged as the star of the show.
The same is true, though in a less heavily slanted way, about Eleven and Amy Pond. He spends their entire run together reacting to the circumstances of her life, rather any impulses or desires of his own.