It won't run 'faster'. It'll just stutter less like Auric said.
As for the video ram...very few games take advantage of more than 256MB of RAM. VRAM is very rarely a limiting factor, as opposed to core clock, memory bandwidth, pipelines, pixel shaders, etc. Unless you were playing, say, Oblivion with some of the replacemement texture packs which are very high res, having more than 256MB of VRAM will not yield significant improvements in performance, for now at least.