I have a higher-resolution monitor if that changes anything. I can run games past-2000 pixels... don't know exactly, sorry. I have a few dollars to spend. If I run two of them, are you sure that the 2GB doesn't do anything better on single-monitor?
The higher the resolution, the more memory you'll need. For that kinda resolution, better off with the 2GB.
As zero_ said, for anything over a single monitor/anything more than 1920x1080/1920x1200 your better of going over 1GB and looking at 2GB cards.