No, you cannot play PS3 games on Xbox.

But for which one is better, it is totally up to you. Xbox is much better in price, but is more likely to have hardware problems. Also, PS3 is better because you can play online for free, and the menus are a lot more user friendly.
Also, some games or specific for the console, such as metal gear solid, it is available for PS3 only. So check the games so that you won't miss out.