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.2GB is more beneficial at resolutions above 1920x1080 only.
1Gb is still enough for 1080p at this current time.
if he can afford to buy an nvidia gtx570 then its more better than both version of ati.You could however go for a nvidia gpu which will have 1.25GB ram (GTX 570).