The VRAM does not effect the speed of the card at all. It is simply there to display at higher resolutions. I would go with a 2GB if you own a 1920x1080 res monitor or higher.
you're right about the speed thing. VRAM has little to no effect on speed (if we are talking about the same era VRAM, GDDR5).
however VRAM is not 'simply there to display at higher resolutions', it is the main memory hold for the graphics device of the computer, and has quite an impact when you're looking at things from a gaming aspect.
ninja; it does also do what you originally said though, the more VRAM theoretically means a higher display resolution