I still disagree that the second game didn't have a good story. I think people are too fixated on the Protocol 10 thing that they forget everything else, when the story wasn't just about Protocol 10, although I do admit that Strange and Ra's could have used more screen time and development.
I think the problem with the way some people judge the AA/AC stories is that they're looking at the wrong story.
In Arkham Asylum, the main story isn't really the stuff with the Joker taking over the asylum; it is Batman in the asylum itself. The asylum is the main villain. The main story is essentially him coping with one of his greatest fears - the idea that maybe he is just as insane as his rogues gallery and belongs in the asylum with them. The Joker story is just the filter used to tell that story and the side stuff (interview tapes, Amadeus Arkham, etc.) play as much of a part in Batman's internal struggle as the Joker/Titan story.
In Arkham City, the main story isn't really the Hugo Strange stuff or the Joker cure; it is Gotham having become the asylum and Batman coping with one of his other greatest fears - that all of this is his fault. That he created his own villains and that part of Gotham now having become the same ****hole of insanity the asylum is has been entirely caused by him. In that sense, Arkham Asylum questioned the (in)sanity of the asylum and its people whereas Arkham City questions the (in)sanity of Gotham and its people. Much like in the first game, what is presented as the "main story" (in this case we have two stories (Joker cure + Strange/Ra's)) isn't really the main story, but simply filters through which the real main story is told. And much like in the first game, all the side stuff are just as important to the real main story as the main stuff. The real main story is filtered through the side stuff as much as it is filtered through the main stuff. The fact that Batman has two major mastermind plots to solve and all the side missions in one night also plays into another theme: that Batman has to deal with all this crap in one night because there is complete chaos everywhere, which goes back to the ideas that Gotham has now become Arkham Asylum and that this is all Batman's fault.
As a side note, I once saw a superhero reviewer on YouTube do an in-depth analysis of Arkham City's story. I'll just leave this here:
[YT]V5lIhVhlmeo[/YT]
He did an in-depth analysis for Arkham Asylum as well.
[YT]yHNr1GuwwUs[/YT]