A GTX 680 with 4GB of RAM in theory lets you play at higher resolutions with higher graphic settings. However, in the future as games become more demanding (as they always do) a GTX 680 won't likely be powerful enough above 1080p resolutions. So getting 4GB may not necessarily make sense at that level.
Having 4GB of RAM makes sense for multiple monitor gaming or just high res gaming (higher than 1080p).
If you don't already have a GTX 680 then don't buy one. The GTX 770 is out, is cheaper, and faster. If you already have a GTX 680 and want a second one then going SLI will boost performance quite a bit. Though I'm not certain a 4GB card plus 2 GB card would actually see any advantages.