7770 is comparable(new drivers) 7850 will blow it out of the water. 1gb Vram vs 2gb Vram, IF the card is fast enough to play the game needing more Vram then yes, but most of these mid range and lower end cards get bottlenecked by thier framebuffer, they have a lack of shaders/rops/tmu etc so they cannot take advantage of more ram anyways. Like having a pair of Z rated tires on an engine that can only deliver B rated speeds.
Personally, 650Ti 1gb is fine, if you want more then that a Radeon 7770 or 7850 are the next best bets, and are def worth the price increase if any. Again, I do not believe it is limited by its amount of Vram but rather the width of the bus the Vram talks on, simple as that.
Enough reviews will point out that 650Ti is not really meant for 1080p gaming at acceptable performance levels anyways, it is more meant for 1680x1050 or less levels to be able to use eye candy and have good frame rates while keeping noise, temps, and power use at a minimum.