The GB has to do with your XB's space to store data. The more GB of memory your XB has, the more games it can save game progress for. It also means the more games and extra content it can download from XBox live (paid of course, but you can also get demos there to try things out), and music you can put on, etc.
If the price isn't all that different, I'd just get the bigger one so you never have to worry about it. Otherwise you'll have flash drives all over with different saves on them you have to track down when playing games.
I don't think the Kinect games would save using any more or less space than other games.