The Batman we all know from the canonized comics of DKR, TLH, Long Halloween and most of his modern incarnations, including the Dini/Timm universe is a really tough as nails, stoic, always knows best Batman, who rarely makes major mistakes or questions the efficacy of his mission. These interpretations, with little exception even in "early batman" stories like Year One and TLH deal with a matured Batman who really isn't that conflicted.
Nolan's Batman is still a young buck, still dealing with his big issues: His angst and remorse at his parents death, and how too successfully fight crime (Batman Begins) and the moral and ethical concerns of justice and vigilantism (The Dark Knight) and of course, Nolans insular neo-realist movie world doesn't provide for the off the wall elements of the comics, or the inclusion of the entire rogues and allies gallery. Thankfully, these movies have been treated as movies, and not comic books, and that's one of the main reasons they're so far ahead of the competition.
I think you need to Broaden the scope of the question you're asking
Are the Nolan films true to the letter of the comics? They sure as hell aren't, and I wouldn't want them to be, the comics aren't even true to the comics, stuff gets retconned all the time, and face it, no matter how great the story is on the page it would look pretty bad directly transferred to the screen.
Is Begins the definitive Batman origin story? With the exception of the third act round-up, I'd say most certainly, and i think anybody who would ever try to retell his origin on film is on a fools errand.
Is the Dark Knight the definitive take on the Joker and the bats vs. joker conflict? without factoring in one one might say about perma-white or origin story, i'd say certainly, it's a take on the character and the conflict that encompasses all of the philosophy and history of this age old battle while giving it a brilliant, griddy twist. It may not be a direct adaptation of the Killing Joke, but without a doubt it pays tribute to it and incorporates all its ideas of madness and justice and corruptibility and conflict in entirely it's own way without sacrificing the impact.
I think the real question is, do these films do the comics the justice they deserve? I think that's a resounding yes. Because even though the film does not follow any specific arc to the letter, it incorporates thematic and plot elements from a plethora of stories throughout the history of the characters and nails them in their dramatic essence while telling A Batman Story that can certainly hold its own against any of the comics it was inspired by, and really, that's the best you can ask for.