512 and 1000 mb basically means more VRAM for your card which is essential and required more when playing games on bigger resolutions.
In your case the max resolution is 1366 x 768 which is decent so a 512MB card will do but there are more eye candy settings like AA, AF and Ambient lighting that occupy more space when enabled or increased on the Video RAM. So in that case 1gb G.card is better to buy.
So to conclude the use of more VRAM is simply greater resolutions and faster rendering etc when using heavy graphics options like AA and ambient lighting etc.
I checked the laptop models and they are same with the difference of only VRAM and i would advise you to buy the 1gb one as the price difference is not that much anyways that is 30$ only.