I have just started playing this past weekend but so far its living up to the hype!
Overall gameplay is the same as the original which is not to say it is really good. I really like the expansive game world and the many places you can look and explore. This is the way to get to access the side missions. While gliding over the rooftops you may occasionally hear cries for help and dropping down to the street you can get access to a side mission helping political prisoners getting beat up or finding a dead body which leads you to investigate who killed him. The streets are full of thugs that you can practice your combat skills on (I know I did). And you will be needing that practice as there are some fights in the main story that will have you fighting about 20 thugs or more at a time.
Playing Catwoman (for me) is a mixed bag. But like I said I've only been playing for a couple of days. I find it difficult fighting as Catwoman. Although others may find it easier. She is quite agile and her fighting moves are cool but her seeming lack of power makes me fight thugs for a longer time than Batman and thus having a greater chance getting beaten. Still fighting really depends on how good you are with your timing and use of take-downs and special moves, and mine admittedly sucks.
I wish I had a better graphics card and a card I can use for Phys X. but even on my old 9800GT the graphics are good. Very little in the way of slowdowns so mo problems "in-game" there. Smoke effects and lighting are good. And the overall look and feel is very nice in that it really makes you feel Arkham city is a gloomy place.
There are 2 main problems that I have encountered so far. One is that the game will (very rarely) crash out to Windows for no apparent reason. I encountered this 2 times. They both occurred while the game was being loaded up. Another issue that I have is that it takes really long for the game to start. The initial loading time when starting up the game from Windows (7) takes a long time (about 4 minutes or so). I'm not sure why this is. I hope it has something to do with my limited RAM (2GB) as i will be upgrading my RAM soon. These 2 issue are the only reason I did not score the game higher.