4 gigs is for multiple screens however I have no idea about the performance limits of the GTX 680 but if it is speedy then the 4 gigs of video ram will help with multiple monitor setups.
same story with the gtx 770 - they're full multi monitor set-ups. If you've got just 1 1080p monitor then you can save money by getting the 2GB version or getting a weaker card.