Ok well here is the low down.
A four Gb card would be better.
When start to play games in a higher resolution above 1080p say.
The textures of the game are of a higher resolution so are more sharper and detailed.
But it requires per texture more memory space.
The memory on a graphics card is there to store all the textures as close to the gpu it can for rendering and display.
Gddr 4 or 5 Memory is a lot faster than DDR 3 system memory.
If you have a card of a lower GB size say 2GB then the amount of memory limits how high the textures can be in resolution or detail within a game.
Each graphical enhancement like AA or anti alias also requires more memory Along with other Fx and again takes up more memory the higher you go in resolution.
Because more information is being processed and sent through the gpu and to drive the display. And Image texture rendering.
Extra memory gives you more storage space and bandwidth or the speed it can deliver Fx or textures.
Also when the memory is limited on a graphics card in order to load new textures it has to be called from the hard drive to the memory of your computer and sent to the graphics card ram for update and storage via the cpu.
As you can see those steps would take more time.
So the speed is a factor to keep things nice and fast the textures ect in a game are pre set and loaded, stored in the GDDR memory of the card for faster access. Or the rest of the system slowing the process down.
You only have to take one step or the shortest route to access the information required.Read it and render, or display it.
Other than going through the rest of the sub systems.
lack of memory results in Jerking because its waiting for the rest of the system
were the textures have to be swapped or reloaded.