Rent it for sure. I bought it and loved it. More open than Arkham Asylum although not quite to the extend of a grand theft auto game. You have free roaming over the entire city though, streets and roof tops. I've barely touched the main mission and have been working on the 400 Riddler puzzles around town as well as some of the side missions. Also special missions that unlock additional equipment/upgrades beyond those you unlock while leveling up.
Combat is the same but they add a gliding mechanic where you can glide around with your cape and then use the bat grappling hook and such.
Also a great story so far.
100% rent and if you like Batman or 3rd person action, Id say definitely consider a buy.