Is Doctor Who Doctor Who, no matter what actor plays him?

It’s a thorny question in certain areas of Doctor Who fandom: is the Doctor still the same person between regenerations? Obviously, the question of continuity of personal identity is one that’s been puzzling philosophers for 2,500 years or so, so in a sense this is nothing new, but in the crazy world of Doctor Who, it takes on greater urgency – individuals can have fads, they can be different in different decades of their lives and experiences can change them, but does regeneration itself change the personality to the extent that the Doctor will do and say things as one incarnation that a previous or future incarnation would never do?

For example, was the sixth Doctor more violent than others? Surprisingly, both first and second Doctors were capable of violence and killing. Jon Pertwee’s Doctor may have known martial arts but Tom Baker’s Doctor apparently didn’t – until Seeds of Doom. Did the Doctor simply decide he was tired of twatting people until necessity overtook him, just as a kid got tired of hobby as he grew older?

Here, at least, is an interesting comparison: it’s Colin Baker reading out Matt Smith’s dialogue from Rings of Akhaten. What do you think? Does it work? Could the 6th Doctor have delivered the same speech in the same way? Would he have?