The higher the resolution in games, the more VRAM there should be since more textures & packs need to be loaded.
Due to technologies such as AA, MSAA, AF, QSCAA.. those really feed on the VRAM depending on the game.
However some cards are not powerful enough to use the extra VRAM. For example there's no difference between HD 5670 512 MB and 1 GB as the GPU itself is weak enough not to handle that amount of RAM which is the case of your 2 GB DDR3 card.
GDDR 5 is much faster than GDDR3 in transfer rates, almost double the speed.
What are the 2 cards you're referring to?