It's a tough question. I think the strongest overall film in the series is The Dark Knight, probably. However, they all have particular strengths and weaknesses that make it tough to judge as a fan.
Batman Begins had the biggest "adventure" element to it, and even though some of it's action was much weaker than Dark Knight (and especially Rises), it really delivers the most value in terms of a traditional Batman adventure. That said, it lacks a strong antagonist because Ra's spends most of his time unknown and off screen. Dark Knight and Rises, by contrast, delivered what I would argue are the two best villain performances in modern superhero films.
The Dark Knight had the strongest script and delivered the most the most drama--even though the stakes were smaller than Rises, TDK was much more of a thriller. It also delivered some staggering emotional content, but most of it was focused on the supporting players--Batman's role in Dark Knight was, really, to be the rock. He just had to endure everything, which while satisfying in the end, didn't provide as strong a character arc as the other installments.
Rises, while not as strong in some terms, delivers I think the best story content of the series, even though it wasn't always executed as strongly as Dark Knight. It was a story much more heavily focused on Bruce, and even though he was only Batman for a fraction of the film, it delivered the most satisfying character arc for him. I also applaud it for being the most daring of the films in that it did something nobody ever does in Batman mythos--write a happy ending and a definitive conclusion. I think the core emotional story about four people struggling to leave their pasts behind was some of the most poignant in the series.
It's hard to really pick one--which is a satisfying problem to have because it means these films fit together really well. Contrary to some reactions I don't think there was much variance in quality in these three films; they were all strong, despite particular flaws in each. Good batch. Satisfying to watch in a row.