When it comes to playing games the amount of RAM you need is dependent on the resolution of the screen. A laptop with a resolution of 1366x768 really only needs 512MB of RAM. 1GB of RAM is not necessary unless you play games at 1920x1080 resolution. More than 2GB of RAM does not make a difference until you hit 2560x1440 resolution.
However, more important than RAM is the performance of the graphics chip itself. Assuming you want to play games with at least high graphic settings, then you need to buy a laptop with the appropriate graphics chip. I don't care how much RAM is dedicated to the graphics chip, it will not improve performance. So a nVidia GT 635m with 1GB, 2GB or 16GB of dedicated RAM will perform the same.
The nVidia GT 635M is just marginally faster than the older GT 555M. That makes it more powerful than the Radeon HD 7670M. How much better depends on the game, it could be at little as 7% faster to as much as 30% faster. I would save on average the GT 635M should be around 15% - 20% faster than the Radeon HD 7670M. Good enough to play many games with high graphic settings at 1366x768 resolution and have good performance (40+ FPS). Of course, the more demanding the game is the lower the performance. Do not expect 40+ FPS in games like Far Cry 3 or Metro 2033.