I bought Arkham city purely based after trying arkham asylum demo a long while back, all i remember was cool combat animations. And i skipped arkham asylum because i heard it was short and not worth $60. the game is cheap now and im considering buying it but would like to know, considering that it is before arkham city, what, if any, big gameplay changes, features are missing (besides the open world feel to it) that make you go, "Arkham city had this, but this game doesn't" (since i played arkham city first)
Not much is really different combat wise, arkham asylum just gives you more of the story leading up to certain events in the second game. Arkham city has a couple of new gadgets but that's about it. Asylum is definitely worth the money though, it's about the same length (campaign wise) as city is and in my opinion it's an overall better game.