Through David Tennant's tenure as The Doctor we never see him pick up a gun or use violence as a form of cruelty (with the exception of "The Family of Blood").
However, when he hears of The Time Lords return in his last episode he takes Wilfred's gun without question (despite rejecting it several times up to that point).
What makes the possibility of the Time Lords returning so much worse than The Master (who by any measure of the term is basically psychotic)?
The Time Lords had changed greatly from the pacifistic race of non-interventionists from the old series.
Throughout the new series, we learned more about the Time War, and how it changed the Time Lords, made them more warlike and dangerous. Under the leadership of Rassilon (the jury is still out if it's the original Rassilon, brought back somehow) the Time Lords were ready to do just about anything to defeat the Daleks.
Problem is, once a group has become warlike and violent, they very rarely return to their peaceful ways once the war they're fighting is over.
His decision to "destroy" (as far as he knew at the time) both races was not a case of sacrificing his people for the sake of eliminating the Daleks; he'd realized that they'd become as dangerous as their enemy.
The Doctor feared that his people had reached the point where they were too violent and too dangerous for the sake of the universe. So much so that he was willing to use violent force, as made physical by Wilf's pistol, to keep them away.
During the Time War, the Time Lords became among the worst civilisations in the universe.
His snatching the gun is already a way to show us how terrible the Time Lords must be. The Doctor also explains this to Wilfred in the same episode, why the prospect of their return filled him with such dread:
WILF: But I've heard you talk about your people like they're wonderful.
DOCTOR: That's how I choose to remember them, the Time Lords of old. But then they went to war. An endless war, and it changed them right to the core. You've seen my enemies, Wilf. The Time Lords are more dangerous than any of them.-- "The End of Time, Part 1" (emphasis mine)
It's worth noting that even though they were changed by the Time War, the portrayal of Time Lord society in the show has never been particularly rosy. In their first ever appearance, they put the Second Doctor on trial for the crime of helping people, find him guilty, and sentence him to forced regeneration and confinement on Earth. The Sixth Doctor also gives them this contemptuous speech:
DOCTOR: In all my travellings throughout the universe I have battled against evil, against power-mad conspirators. I should have stayed here. The oldest civilisation, decadent, degenerate and rotten to the core. Ha! Power-mad conspirators, Daleks, Sontarans, Cybermen, they're still in the nursery compared to us. Ten million years of absolute power, that's what it takes to be really corrupt.
-- "The Ultimate Foe" (emphasis mine)
The Master is psychotic, yes, and he's essentially destroyed humanity by grafting himself onto everyone. But the Time Lords are (now) an entire civilisation of psychotic war criminals, with all the power of Gallifreyan society, which is said to be the most advanced in the universe. They could do far worse than one single Time Lord could. And indeed, they do try to do far worse: "the end of time itself" (whatever that means) will affect a lot more than just one planet, no matter how much the Doctor cares about that planet.
I disagree with the notion that David Tenant's Doctor never used violence. Although The Doctor across all his regenerations generally prefers a non-violent solution, the Tenth Doctor in particular developed an attitude of giving one warning, after which he was prepared to kill. We saw this in his debut episode 'The Christmas Invasion' where he deliberately caused the Sycorax leader to fall to his death. He then says "No second chances. I'm that sort of a man" which implies that, following his regeneration, this is a new or modified aspect of his personality. Another example is 'The Runaway Bride' where he slaughtered all the Empress's babies and says "you did this". Later, Donna says that she was scared of him, because he watched them all burn and he just stood there watching. It was also implied on a couple of occasions that travelling alone was a bad idea because he was capable of terrible things without a human companion to temper him.
Generally though, The Doctor's pacifist stance is in contrast to the rest of his race, and therefore relative. He has evidently made his own code of conduct to live by, not taken from his race, and not easily pigeonholed. Since the Time War, The Doctor appears to regard the Timelords, on the whole, as the most dangerous race. This is primarily because of what he believed they were going to do to end the Time War. We know that in his "in-between" incarnation as The War Doctor he was prepared to kill all the Timelords and Daleks together using The Moment/Eye of Discord. Although his pacifism was effectively removed during this incarnation by the regeneration given him by the Sisterhood of Karn, he was only driven to this choice after fighting for over 100 years and seeing no other way to protect the rest of the universe.
The Doctor would also know that, given he killed all the Timelords (at this point in The Doctor's timeline Gallifrey had not been saved by him) and that this event was "time-locked", any new encounter with them could only be by them breaking out of the time-locked war period.
So it isn't really out of character for the Tenth Doctor, who is already prone to "justifiable" violence, to take up arms against what he considers to be an enemy of the rest of the universe, and an enemy which he had already killed.
