The 1GB version not only has more memory, but also has a higher bitrate, and more ROPs. So it will perform better anyhow. At low resolutions, the 1GB is not a requirement by any means, but personally I'd go for the 1GB. At 1680x1050 or higher, with high graphics settings, the 1GB of RAM could come in handy depending on what you're playing.
For example, GTA IV really likes high RAM amounts on video cards.