Honestly, the 650Ti probably doesn't have enough muscle to actually use 2GB of VRAM, at least not in those games. The 7770 and 650Ti would both run out of steam before hitting the VRAM limit with 1GB.
GTA won't run that great regardless of what card he has, and BF3 needs something stronger than a 7770 or 650Ti before it will go past 1GB of video memory. The only game I can think of where the 650Ti might benefit from the extra memory would be Skyrim with the high res texture pack. With every other game that uses more than 1GB, the GPU will be what holds performance back, and not the memory size when dealing with this class of cards.