eryx raised this over on DWAITAS. When you regenerate, are you as Steven Moffat puts it "the same man with a different face" or as Russell T Davies puts it "a different man goes sauntering away"?
Now, I'm tiptoeing around things covered by the NDA for The Time Traveller's Companion here, as regeneration gets a big new writeup, but I can safely say that it addresses some of the different ways of looking at it.
Because the answer to both options above is "yes... kinda".
The Doctor is notably worse at regenerating than other recurring Time Lords, because they can be played by similar-looking people for ease of recognition much more easily than he could. But I must admit I've never been able to get past the out-of-character reasoning and suspend my disbelief on this.
So when Kai regenerated in the finale of The Door In Time he came out looking like himself after losing a bit of weight and getting a haircut. (And Effie, who was standing a bit too close, lost forty-three years of age, but that's just one of those things...) So I suppose that's how I'd play it, unless I had a hefty reason not to. Watch as I deviate from canon because I don't have to worry about finding a replacement actor!