Irrespective of the resolution, between a 1Gb and a 2Gb VRAM card, ALWAYS go for the 2Gb VRAM (especialy when we talk about CoD...)!
I presume there is no significant difference between the 1Gb and the 2Gb...
The min VRAM you should have for CoD should be 1,5Gb. Any less and you tend to see the limits (and start thinking of shortcuts).
~S~
PS. Sombody mentioned correctly, check the limits of your power supply! As you wrote, it is a proprietary PSU thus you may not be able to change it and you may be very quickly limited by the Wattage your PSU can deliver...
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