I assume your question is concerning the 1GB 6950 as this seems the viable comparison. Here is a direct comparison: http://www.anandtech.com/bench/Product/290?vs=331.
For resolutions below 1920x1080 you are unlikely to see a big improvement with 2GB VRAM vs 1GB VRAM as your never going to be bottlenecked by the display buffer width. At those resolutions best bang for your buck would be CF6870's which come in around the same price as the 2GB 6950 but will outperform it on a single monitor system.