There's been all that talk in "The Parting of the Ways" & "The End of Time" about whether or not the Doctor will still have legs or a head when he's done regenerating. And yet, all of the other Time Lords we've seen have been very human-looking. Here's my theory: Regeneration requires some effort and it's really dangerous. If you don't do it right, you end up deformed, possibly permanently. You can have some control over it but that depends on your degree of skill. When the Master did it in "Utopia," he just kinda went for the idea of being younger. The Doctor, of late, keeps trying to turn his hair ginger but is so unskilled that he just kinda has to settle for what he gets and focus most of his mental energy on the basics. Romana had more control over her regeneration because she is more skilled but it's still dangerous. (I mean, you could accidentally cut your own throat while shaving and bleed to death but it's a very minor risk if you know what you're doing.)
As for the change in personality, I think the brain ends up essentially the same. However, it's kinda like stuffing all of his memories into a bag, shaking them up, and spilling them out again. It's the same contents but in a radically different configuration.
When the 9th Doctor regenerated in a giant shower of CGI sparks, at the time, I attributed it to his body expelling all of the time vortex energy that he absorbed from Rose. But then they kept using that effect, so now I don't know. (Especially since, when I try to come up with rules for the Doctor & the Master, I realize they they don't necessarily account for River.)