I liked Asylum a bit Better, it had more of a Metroidvania feel to it which I liked. And even though City was more open you still didn't explore Gotham. You just explored a bigger more open arbitrary island. I thought the story was a bit better in Asylum.
Play whichever one looks more interesting or both. The stories are spoiled a bit if you play City first, but I the plots in both games are quite predictable and doesn't get near as interesting as the animated series did. The character interactions with the VA's from the original series is the more interesting thing to me. But, the story is still quite enjoyable.







