It's so un-Doctor-y to me. That scene grates a bit. Though the Vanity Doctor would be the one to throw a temper tantrum about that shit.
For my money, the single most powerfully acted scene in the show's history is Catherine Tate in Turn Left just before she's sent back in time. Her terror is so palpable. It's a stunning scene. Not even Rose could kill it.
Yeah, definitely this. Catherine's performance there is the finest Doctor Who has EVER seen, IMO, even the old show.
If we're talking Vanity Doctor, I think Tenannt's scene in the cafe is actually better than his raging against the dying of the light scene.
https://www.youtube.com/watch?v=3Rn77V1tG38 Such a magnificent performance. Cribbins, too. Moffat did accidentally add something to that scene, though - in a sense, it can now in hindsight be viewed as the Doctor raging about going into his last life, too.
Mainly, though, I like to think it's about how RTD structured his series as well as the overall vanity of Tennant's Doctor, which was instilled by having Rose and Martha both worship him. Tennant's Doctor is, without doubt, the shortest-living in terms of actual days/years. Smith is actually the longest now, which is interesting.
Every other one lives for a couple hundred years, or at least a human-ish lifespan, a few decades. The tenth Doctor lives for five years, the series makes it plain... the justification is there. I think that really gives reason to why he rages, to be honest. Of course Smith regenerates triumphantly; he's lived for hundreds of years, longer than any other life, AND he's just dodged absolute death, so of course he's happy... whereas I like to think Tennant's Doctor really feels his time comes too soon.
Or to put it another way, d'you imagine that when in Day of the Doctor he learns that Eleven is 400 years older, he thinks that he'd only make up six months of those years? Eccleston quite possibly/probably has a similarly short life span (though we'll never truly know), but the difference there is that Eccleston's Doctor has a death wish from the word go. He wants to sacrifice and die, he thinks he deserves it. Tennant's Doctor has things to live for. Or... he does, but then every time he finds them, they're ripped from him.