I think, in these movies at least, they're both
the disguise. We know the Bruce Wayne the public gets to see, the wise-ass, babe toting, speeding, ignorant to world events playboy, is a "disguise" and not the "real Bruce Wayne. Batman is a disguise because as Batman Bruce Wayne has to act and behave in a manner he doesn't agree with and even go to extremes (the listening/"SONAR" device, to accomplish his goals.
But then we've the "real" Bruce Wayne. The Bruce Wayne he shows Lucious, Alfred and Rachel. In these movies Bruce is never really "himself" except when he's with these people and even then only when his guard is down.
I think Harvey Dent's "change" makes some
sens but, really, needed some more pushing. We see how "unstable" he is in the scene where he has a captured Arkham patient in an alley and is questioning him about The Joker. His use of the coin also shows how much Dent likes to manipulate people. But he was overly sold as nothing more than a slick, smooth-talking, D.A. who was good at his job with a hint or two of an "edge" (again, the alley scene) but yeah his turnabout into Two-Face seems pretty quick. But it's possible the death of Rachel, the betrayal of the police (most notably Gordon not taking Dent's word that the men in MCU were crooked), the betrayal of Batman (with the apparent saving of him rather than Rachel) and his horrible disfigurement was enough to just push him over the edge. From his POV he had pretty much lost everything he wanted and had worked for and, not only that, he was horribly disfigured. So it was time to get his revenge on those who hurt him.
Though I agree it would've been nice if the last we see of Dent is when he reveals himself in the hospital and then as the movie goes on we just presume him dead in the explosion, he gets revealed in a final scene and then we use him in the second movie. Because, Eckhart did a really good job with the part and, really, needed a whole movie to flesh things out better.
The Hong Kong scene was a bit gratuitous, but fun. Although it has "International Incident" written all over it.