In the beginning of the Batman mythos, he used a gun to kill.
In Batman Begins, he didn't save the archvillian from a speeding train though it was of no certainty that he would have been successful.
Nolan intentionallly bookended this.
When the monastry blew up, Bruce risked his life trying to save Ras/Ducard.
When Ras when in Wayne Manor, Bruce told him that he saved his life.
Ras remarked, "And I warned you about compassion."
So clearly Nolan's Batman is not a creature of compassion. Sure, Bruce Wayne is but his Batman creation learn in BB to be less compassionate and more justice oriented.
Nolan has Batman say on the train,"I won't kill you, but I don't have to save you. Guess what? He's right. Batman is not a police officer, not a boy scout, and not Superman.
Bruce knew he saved Ras before and as a result, many in Gotham almost died. If he saved him from the train, Batman knew that next time Ras may be successful. Bruce's goal is to show the people of Gotham their city doesn't belong to the criminals and the corrupt , to save the people of Gotham...even at the expense of not saving those who would destroy Gotham. (Kinda makes sense doesn't it?)
But make no mistake, Batman is not an executioner. Even Nolan reminds the audience of this.
The character was not originally invented to serve that role, he was created to be a vengenful ceature of the night that criminals feared. Maybe the Batman character has evolved from this origins since then AND maybe Nolan's Batman will evolve too as the series progress. But I think its appropriate the Nolan has in many ways started this series at the character's roots.
But is Nolan saying that his Batman represents Venengence? NO. He starts out that way, just like the character did in the comics, but he grows from that into a symbol of Justice. Why did Batman leave Ras on the train?
Justice.
Nolan's Ras states, "Justice is balance. You burned down my house and left me for dead. Consider us even." after Bruce is knocked unconscious and left for certain death in a burning house.
Well, now Batman flees a train headed for destruction and leaves Ras for certain death (?) (Of course nothing is certain in a comic book movie).
An ordinary man would have saved Ras because of our compassion. Even he said, "You are just an ordinary man in a cape! That's why you couldn't fight injustice and that's why you can't stop this train!" It took an extraordinary man to do what Batman did."
Now you may not agree and call B.S. on this. You may say that, 'Right is right and wrong is wrong and Batman should have saved Ras.
Well, even Bruce said in the movie, "The first time I stole so that I wouldn't starve, yes. I lost many assumptions about the simple nature of right and wrong.
And Ducard told him, "Criminals thrive on the indulgence of society's understanding."
Also throughout the movie its clear that Nolan is demonstrating the Bruce/Batman is being moulded into the legendary Dark Knight we all know and love. Moulded by Rachel, by Falcone, Ducard, Alfred, and thru trial and error.
Alfred states, "Well, we both care for Rachel, but what you're doing has to be beyond that. It can't be personal, or you're just a vigilante.
If Bruce would have taken it personally, he would have saved Ras because in spite of everything, he still has a father figure to him that he cared about.
Saving him would have been the easy thing to do, but like a Judge who admininsters Justice, he put away his personal feelings (his compassion) and made sure that Justice was served, because Ras asked Bruce, "Have you finally learned to do what is necessary?"
Well yes, Batman has.
Not that it matters in this discussion but Ras clearly had a deathwish.
Batman: It ends here.
Henri Ducard: For you and the police, maybe. My fate however lies with the rest of Gotham.