2GB is more beneficial at resolutions above 1920x1080 only.
1Gb is still enough for 1080p at this current time.
Plus that, there are some exceptions Due to technologies such as AA, MSAA, AF, QSCAA.. those really feed on the VRAM depending on the game so the more VRAM the smoother the game is. If you're gonna play the new GTA IV with 1 GB of VRAM, you'll be disappointed.
So i recommend you to get the 2GB version.