10 Still went nearly off the rails bonkers in a very short period of time even though people like Martha turned out ok. He didn't have a terribly huge amount of tragedy honestly as even Rose ended up having a happy ending in the end. Donna was the only one who got screwed.
Like I said previously, the point isn't "did people turn out OK" - they all do - but more the effect it has on him. Like with 11, Amy & Rory live on to their 80s/90s, but he's still obviously hugely gutted and upset. The same is true of 10, but it just happens over and over again, and on top of that happens in a really short period of time. Not just the main six companions, but even the potentials he meets - Astrid, Joan, Jenny, The Master, even River - every single one blows up in his face to a degree that just hasn't happened to any Doctor before or since.
This compounds with the fact that he's the most emotionally intense Doctor - likely caused by 9's relationship with Rose - and it's a recipe for disaster. It's not that Martha turned out ok, or Rose got her Doctor, or that Joan remarried, or that Donna gets her millions - it's that after everything he's left with nothing, again. And being left with nothing is an echo of the war that he can't live with, so it drives him off the rails. It'd do that to anyone.
Not arguing that Tenant did not do a great job with those two scenes, but there's a huge difference between simply regenerating (and we had no evidence that 10 thought it would really be his final death), and 11 finding his actual tomb and confronting the end of his actual life throughout all of his regeneration. The magnitude isn't even comparable, even with 11 having lived out his life (and dealt with loss much more eloquently than 10 ever did).
Script:
THE DOCTOR (CONT'D)
I'm going to die.
Silence.
WILF
Well. Me too, one day.
THE DOCTOR
Don't you dare.
WILF
I'll try not to.
THE DOCTOR
But I was told. He will knock four times. That was the prophecy. Knock four times, and then...
WILF
I thought... when I last saw you, Doctor, you said your people can change, like, your whole body...
THE DOCTOR
I can still die. If I'm killed before regeneration, then I'm dead. (pause)
Even then. Even if I change... It feels like dying. Everything I am, dies. Some new man goes sauntering away, and... I'm dead.
Wilf now looking at him. Then looking out of the window.
Then looking at him. Then out of the window.
Think the implication here is he simply doesn't know. He flat out says "if I'm killed before regeneration, I'm dead," and THEN goes on to talk about regeneration, saying before "Even then." He doesn't know. This is pretty clearly telegaphed later in lines in part two, as well. When he flies in that ship, he thinks he's going to death, not regeneration. He is shocked when he's alive at the end of it all. When Rassilon snarls at him "You'll die with me, Doctor," and he says "I know," accepting it, he doesn't think it's regeneration coming, because obviously Rassilon's aim isn't to make him regenerate, it's to kill.
I'm also going to go ahead and question if 11 handled his traumas that more eloquently than 10 on a base level. If we look past the regeneration - which like I say is a different circumstance for a different Doctor - and instead look to simply, say, losing 'their' companion, one goes and sulks for a couple of decades and takes on a scrooge persona, while one is depressed but does keep travelling. They ultimately compound for the 10th Doctor and make him implode, though.
9 was the closest to the trauma of the time wars and lasted even less time than 10, yet he still found it within himself to celebrate his time as this version of himself and to be bigger than his sense of self in the moment.
In contrast from 10, I can't recall 11 dnot embracing death with dignity even from a very young age (almost to the point of fatalism). From under a year in
'The Big Bang'From,
Let's Kill Hitler,
'The Rings Of Akhaten', and I'm probably forgetting a few. Though the point is, that people are being harsh on 10 because he devolved into exhibiting some or the more negative emotions and expressionism, where as 11 was a class when he started and a class act when he left under circumstances that seemingly 10 would have reacted much more poorly under. 11 feels like a genuinely uplifting, warm, and caring person.
I think it's pretty clear that 10 raged on account of his growing ego and sense of self importance. They even take a dig at it in the Christmas special when referencing the self regeneration of 10. He wasn't so far gone that he wasn't still going to do the right thing, but as we'd seen in Water of Mars, he was starting to get there.
9's different because the character has a death wish and a martyr complex all series. He wants to sacrifice himself because it's what he thinks he deserves, and that's why he does what he does at the end. That and love for Rose. There's plenty of examples of the 10th Doctor doing the same things you just linked as 11 (a bizarre one comes to mind, offering himself up to the Daleks to stop them killing the people in New York, but there's plenty more) - that's a key trait of the character. Some more than others. But in the end, what happens to him and the way he goes is a great personal tragedy for him, and that's what makes him how he is in those final moments. He's emotionally charged to begin with, tragedy after tragedy makes him even sensitive and drives him over the edge (and this is visible as early as The Runaway Bride, underlined in Turn Left) and then four/five years simply wasn't enough for him. And who would it be?
Moffats bigest flaw, imho, in all his run was that he was aiming for the Doctor to seem like he is in peril. That is not what Doctor Who is, for me anyway.
When I listen to the Eight Doctor Adventures audiobooks, there are places on the verge of destruction, rotten to the core. Then, the Doctor comes in, reveals the problem or deals with it to the best of his abilities. The drama is that he sometimes loses. Sometimes, there are no saving planets.
This is true to the Doctor Who TV show as well, to a certain extent. You cant save everything and everyone. The Doctor can always save himself, as seen in Pompeii, or even in Waters of Mars, but when a tragedy is about to occur: that is the real drama. The world is the main character, not the Doctor. The setting, the place where the stuff happens is the center of the drama, not the Doctor. Some more examples of this: Impossible Planet/Satan Pit (literally a drama unfolding). Midnight. Mr and Ms. Smith. Vampires of Venice. Blink (partially, though). Gridlock. Beast Below. Rose. Eleventh Hour (partially).
I hope Doctor Who takes this as its new direction. Time to turn the show once again into a drama, a thrill worth watching without having to endanger the Doctor first.
This is my biggest problem as well, but ultimately this, and the whole "Doctor Who" arc, is what Matt's era has ultimately been about. It is what it is now. I always think the program should not be ABOUT the Doctor as much. I mean, when the show began, Ian was really conceived as the lead, and to be honest, regardless of whoever's name was first on the credits, Rose was the star of that show in 2005, and it would've have worked without Billie. Chris leaving was a blow, but I honestly believe had the roles been reversed and it'd been a new companion for Series 2 the series might've died. Billie carried that show. I'd like the Doctor to be less central to everything under Capaldi, certainly, and perhaps with him being an old series fan he himself will influence that now.
I think a lot of the last few years have been down to ego, in a sense, anyway. Like, Moffat wanted to be the one to fix the regeneration thing and I'm guessing he has no idea if Capaldi will outlast him, so he's jumped a few hoops to make sure he was the one to do it. He has wanted to leave his mark by making revelatory things about the character (marriage to River, etc) because he's a fan, and he wants to make sure he's remembered, I think. RTD probably would've done the same but didn't have to, because in bringing it back the man has secured his place as Who royalty alongside Lambert and the like.