There's one thing about Doctor Who i really don't understand. Is each incarnation of the doctor really the same person in a different body? If so then why was the 10th doctor so unwilling to regenerate? And why does the 11th doctor greet Sarah Jane and Jo like old friends if each incarnation of the doctor really is a different person? I'm confused.
It's the same man with a new face and a new everything. That said, his brain does regenerate too, and with it so goes the old personality. There's the core of the man there, absolutely - you could recognize certain things about The Doctor without any acknowledgement of what version he is - but much of his personality does shift and change.
Some new man does go "sauntering away," as the Tenth Doctor says. It still is him - still the Doctor with the same thoughts and memories and all the rest - but the personality is different, the old one gone - and so how he processes and reacts to those situations is different. ("I hate bow ties," the Tenth Doctor says!) You can hear it, brilliantly, in both The Christmas Invasion, New Earth and The Eleventh Hour - these are episodes written as a bridge, and you can hear many lines in these three episodes that feel like they've fallen out of a script for the previous Doctor. I really love in particular the "It is gonna be... Fantastic" (the only time he says it), and the "I'm the Doctor and I healed them," speech at the end of New Earth, which 1) sounds incredibly like The Doctor Dances in its tone/delivery and 2) very unlike the Tenth Doctor we see later on. In the Eleventh Hour, there's a very gradual sort of shift... the Tenth Doctor sort of leaks out of him through the episode. It's wonderfully written and played.
That's why it's a traumatic experience in general. The Tenth Doctor probably would've put on a braver face in different circumstances, but was alone and a bit bitter. He was a very sentimental version of the character, too, and was very found of being who he was. If he'd had someone with him or hadn't died so soon (based on the ages stated in the show, The Tenth Doctor only lives for five to six years, whereas the Eleventh already has several hundred chalked up off-screen) he'd probably have been much more different.
I imagine for instance that if Rose hadn't been there the Ninth Doctor wouldn't have been so triumphant, he'd have just raged or quietly accepting. It was being alone for him more than anything, I think. Only the Seventh Doctor died alone, and that was relatively quick, as he was literally shot in the heart by LA gangbangers (lol) and then died in theatre as the humans operating on him did more to hurt than to help. He doesn't have a chance to be sad about dying alone, as he spends his final moments panicked and pleading with them
not to operate on him before being sent under for the procedure.
For some more information on regeneration, though, we can look to the classic series. The second Doctor's regeneration is forced on him by the Time Lords, for instance - it's a punishment for meddling where he shouldn't. The Time Lords actually give him the choice of several faces, and the second Doctor refuses, he says he hates them all. They force it on him anyway (implications of this for if the Doctor could choose his own face, too) and he goes screaming, because he too didn't want to go, and he felt he was being dealt an injustice.
I do wonder if Matt'll be graceful or not, especially as his personal favourite Doctor is the second, and he asked Moffat to build a lot of his base 11th Doc characterisations around him. Eleven is as bumbling, clumsy and lightly emotional as Two.. and two kicked and screamed more than any of them. It was a shit way to go, mind.
Regeneration is a sticky old subject, really, but it definitely is the same man, yeah. But, really - imagine your personality and appearance was going to be wiped away! It's not exactly a nice thought, even if you get to live on. What if you come out the other side a psychopath? He almost did that too, really, with his sixth incarnation.