I agree with you mostly. What I did like better about AC is the combat. Everything seemed more fluid and there were more options.
Also, playing as Catwoman and Robin was tons of fun. They weren't radically different from Batman, but it did add some variety.
Finally, regarding the "open-world". The major plus of AC over AA is the ease of getting from one place to another. Think of the city as more of a hub to the minor levels than as one big sandbox. I found it to be tedious getting from one end of the AA game to another. Plus, any fan of Batman has got to at least see some appeal to flying about a city at night, dropping from rooftops into a crowd of thugs.
This! Yep. I was worried I was misremembering but AC's combat was more fluid and had more options. I rather enjoyed Catwoman's challenge levels; it was a different style. I don't remember Robin at all (wasn't out? forced myself to forget?).
YESS. I crossing the AA map got tedious quickly. I really enjoyed boost-gliding over the AC rooftops, and getting to place again (e.g. for collectables) wasn't a pain (well, up the tower took a little bit). I really loved the "getting a drop" on thugs. It felt very batman-y (though my Batman media is limited a the 90s movies and a few episodes from the '60s series.)
My main problems with AC had to do with the story, which relied on too many implausible (yes, implausible in a Batman context) coincidences and twists, and an inherently stupid concept (Arkham City itself.) I also didn't love the open world, it was thankfully easy to traverse but kind of hollow and pointless. And it gets real old, real fast hearing random inmate chatter about how cold they are or how much they want to bang Catwoman or Harley.
Yes, the AC premise was outlandish, but meh and move on and enjoy it for what it is. It's a comic book anyways, realism is out the window. (e.g. batman can't generate enough aerodynamic lift from his cape, to boost-glide, but that doesn't mean I don't enjoy boost gliding). Were you expecting balanced debate over whether Debussy or Ravel had a greater hand in shaping Impressionist music?