Tim says:

Full install basically makes it so that the entire disc (movies and all) are on your hard drive. I've never done it that way (multiplayer is all I use it for) but if you are one of those people that just has to see the movies, go for it. But if you are trying to conserve space Multiplayer install is really the thing you want. It will give you the option to put in the disc to watch the movies when the time comes, and give you the option to hit "cancel" and just skip the movie.