Superb Batman Action
This is a step up from Arkham Asylum. You're now roaming freely through Arkham City, which is huge compared to the Asylum. And it performs a lot better as well!
It's everything that Arkham Asylum had, in a much larger area. Flying through the city is a joy, especially after you upgraded your gear a bit. Alternating between Batman and Catwoman adds some nice variety, as each has their own play style. The Catwoman arc could've been fleshed out more though, especially the last part.
However, I consider the story weaker than Arkham Asylum's. There's just too many big shots trying to play an important part in it, which ends up downplaying them all.
And unfortunately it isn't friendly to women. Being insulted as Catwoman is just one thing, it makes sense. There are two other woman that play an important part (not Poison Ivy, she's minor). While these characters are exceptional and even recognised as such, when they are on screen they end up being weak, frail, gullible, and one is unceremoniously offed.
Still, it's loads of run just flying and sneaking through Arkham City, collecting Ridder trophies, and brutalizing terrified bad guys a dozen at a time.