The gigabytes in your gpu is the gpu's ram. (vram) It's used for storing information that needs to be accessed quickly. However 2gb will be just fine for any game at 1080p. However if you're running at 1440p with antialias and such 3gb and upwards can be worth it.
If you're running 1080p or mild 1440p like most people it would be best to stay at 2gb as your gpu would be to slow anyway once games actually starts to take advantage of the extra vram.