BloodHK47 :
Well just asking this because of same games that require a large video card memory such as GTA IV. Not related to it or thats just the memory core clock itself? And so VRAM just deals with if your using more monitors thats all?
Check this benchmark:
http://www.tomshardware.com/charts/2012-vga-gpgpu/09-GTA-IV-EFLC-DirectX-9-C-Extreme,2957.html
Even at extreme settings with resolution 2560x1444, the extra memory doesn't really help. there is <1FPS difference between the 1.5GB GTX 580 and 3GB GTX 580, and a less than 0.5FPS difference between the 1GB 6950 and the 2GB 6950. In both cases, the difference does favor the card with more memory, but it's not noticeable.
Even today, 1GB is good for 1080p. 2GB is overkill unless you are stepping up the resolution with multiple monitors, so you can consider the 2GB your future-proofing.
There might be a case to go for more memory if you intended to SLI/CrossFire along with multiple monitors, but single GPU and single 1080p monitor, no reason to have more than 1GB of memory, much less 2GB.