TDK is my favorite film of all times. (Interstellar is the second one, I'm in attunement with Nolan's way of thinking it seems. I love The Prestige and Memento.)
It's all IMO, of course.
First off, Nolan is a intellectual. He's interested in psychology and philosophical standpoints of his characters and he explores those by means of the stories of his films. He's really a classical philosopher, he uses a dialog a lot to express things, like Plato, he's verbal. Characters in his films speak a lot.
I've noticed there are two kinds of films in this regard.
Films like the ones from Nolan or Garland's Ex Machina, where you have a lot of exposition through dialogue. Characters take actions which you also have to interpret but they speak a lot too.
The second kind are films like Scott's Blade Runner or Miller's Mad Max: Fury Road. No much talking, characters are revealed much more throught action. Me personally, I like the first approach much better since I like ideas to be presented in the most clear way possible, just Descartes' "clare et distincte". Words are ambiguous too, of course, like any kind of action, but what I like about words and sentences is you know the meaning is there because it was clearly said. Every character takes actions and you can over-interpret that to your liking but that does not mean the film or writer or director meant it that way and that the film is actually that deep. But when character says something it's right before you and you clearly see it was an intention of the artist to have that idea there.
So in Nolan's films you have action side of things which presents the character and dialogue side of things which presents the character. And both levels are rich and complement each other in a very thoughtful and deep way.
That's another thing that's important. The depth. Nolan as an intellectual is interested is deeper meanings and he likes his films complex, layered (go see The Prestige several times, the amount of interconnected things is just insane). So his characters undertake meaningful actions to reveal their psyche, they articulate their thoughts explicitly by means of the dialogue, those things and their meanings are frequently interconnected with other things in the story so they acquire allegorical and metaphorical meanings and all those things are about philosophical and psychological issues of the characters. There's a clash of ideologies, a dissonance between protagonist's view of the world and what the rest of the world suppose it the case, a strungle inside the character's mind, his obssessions, fears, rules, demeanour and quirks he thinks he must not abandon, etc. So it's
form and substance in his films, and that's fantastic. Substance is profound and form is exceptionally!!! well crafted. But this applies more to Prestige or Memento which are non-linear. But although Batman films are linear the work with plot lines is great. Nolan's just a great storyteller.
You can find some analysis of his Batman films on YT and forums and some are really good or at least they can show you something you haven't noticed, etc.
So, Nolan is a very intelligent auteur, who is genuinely interested in the characters, in exploration of their personalities, mind-sets and their relationships to external world and other beings, who's a genius at writing scripts, who does never let form outweight the substance and want his stories to be about something substantial and who's a great storyteller. That's what went right.
And I should mention he loves noir films, Following and Memento were heavily influenced by them so no surprise he was able to make a great Batman grounded in reality.
And what does the DCEU really need to learn from it?
That there's only one Nolan.
The only Batman film I like more than his non-Batman films is TDK, which is just totally different category from other comicbook films and IMO no studio producing CB movies was able to come even close to the quality of this film, it's just completely another level. Something close could be Days of Future Past, but look the Apocalypse. So much worse film I cannot even believe it was done by the same people (well maybe Vaughn was the essential part that was not present at Apo). Some people say Winter Soldier or Civil War was close or even better, but I really don't think so, they are not even close, IMO, and I thought DoFP was overall better film than those two. And I thought writing on Nolan's Batmans was more interesting too. To me it feels he just handles characters and things they say in particularly interesting way which makes those films more appealing to me. I was never able to connect with Marvel characters like with Nolan ones. The things Bruce or Joker or Bane say feel much more intense and visceral, with more gravitas. I felt something like that in DoFP. And Whedon was able to accomplish something similar in AoU, but the overall feel of MCU does not let those words to have the same impact. DoFP was more serious so those sentences felt more appropriate. But Joker's lines or Bruce's line are just pure gold, I miss something like that in other CB films.
MCU is great at what it does but I don't think what it does is so great. Sony had their DoFP which was excellent and First Class was very good too. Now what DCEU should learn from all of this? I'm really not sure. You need the right people to make those film and to run the company, how to detect them, find them, treat them, I don't know. If the rumors about how many directors were approached by WB to direct MoS before Snyder got it are true then I don't know how to interpret that. When so many talented people say no to direct the Superman film!.. And when you try to bring in somebody young and new that feels even more dangerous.
When somebody like Nolan comes to you, a man who wrote and directed and was able to finish the production on Following (what a perfectly written film) and ****ing Memento!, who is inventive and clever, and who wants to work with you because he is interested in characters and has a vision of what he wants to do and ability to make it work, etc., you just provide him with all the money he needs and don't interfere with what he's doing! You as a studio should respect the artist, I think the BvS and SS situation with multiple cuts and rushing things, etc. is unacceptable. In the end it hurts the films, the artists, all those companies involved. I know they want to catch up with Marvel, but this approach will not get them there. I think Snyder, Terrio, Ayer and competent artists, just give them more time to work on script, etc. I mean Ayer had to write SS, will all those characters, in 6 weeks! What the hell...