Generally speaking 1GB starts to make a difference at 1920x1080, but as mentioned above it depends on the game. For some games it may be 1600 x 900.
It also depends on how fast the card is. For example, the Radeon HD 5670 does not really gain any performance going from 512MB to 1GB of VRAM except when the resolution is set to 2560 x 1600. The 1GB version gets 1 or 2 more FPS than the 512MB version; however, the HD 5670 is too weak to handle that resolution. Therefore it doesn't matter if you are getting 11 or 13 FPS because either way, games would be unplayable.
then what will be the scenario if i use 5670 <512mb or 1gb> with i3 2100 and maxx out crysis 2 at 1366x768 with <no or yes(2x)> AA,AF,VSync.
(looking to purchase the same - being best on my budget)