In an easy way:
In cheaper models and in the 7900 range (7900gt vs 7950gt) the 512 configuration doesn't bring benefits because the gpu isn't fast enough to render the data stored in the memory, so there may be no performance increase. When the gpu is powerful enough:x1950xt (xtx with 512), 8800gts 640 and above it renders the data stored in the greater amount of memory.
It all depends on the game itself, the resolution and filters applied (AA and AF) and the power of the gpu core.
The cheap models like x1600 and beyond with 512 mb of ram are sales gimmicks.