I'd say it's TDKR, if only for the final 5 minutes.
Originally I would have said BB is his most emotional in terms of how much emotional context is presented to the viewer. All of Nolan's films are emotional, but they sort of present that in different ways and in different levels.
TDKR definitely takes the cake. Each film in the trilogy deals with a different Bruce's journey is ending and all of his pain and self-repression sort of comes to a head in the film. If you think about it, the entire film is actually about how most of the main characters are all dealing with large amounts of pain or with some sort of trauma in a very short amount of time.
1. Bruce is the biggest victim of that.
2. Selina is dealing with the pressure of her criminal record and wants to escape it.
3. Gordon is dealing with the guilt of the The Dent Act, his family leaving him, and holds himself responsible for the security of the city.
4. Bane is constantly dealing with physical pain, it's his weakness, and he possibly feels responsible for Talia.
5. Talia is sort of dealing with the trauma of losing her mother, of not accepting her father because of him not accepting Bane, and of therefore trying to alleviate that pain by taking her revenge.
6. Gotham itself is dealing with several things at once, the truth about Dent being revealed, Bane's domination, and a possibly a dystopian future.
I would say, at least for now in my understanding of the film, Blake is the only exception to this rule, because although he was an orphan and feels sort of responsible for the boys' home, he is the film's constant, who remains optimistic and hopeful, maybe that's just a thematic sign of him becoming the next "hero of Gotham".
The emotional implications of all of those things are huge. Not only is Bruce's story incredibly tragic, but then Nolan hits you with this entire backstory to Bane and Talia, which is just as tragic. It's beautiful emotional storytelling.