Like a few others have said, 256 mb of Video RAM versus 512 mb of Video RAM, the difference in performance is tiny if noticable. I remember reading here that the idea to market the higher video RAM is just another market strategy where people who don't know the difference would obviously go for the more expensive card (usually with more RAM as well) even though they won't notice much of a difference. The difference really matters when you're playing in higher game settings. Like another poster above me said, video RAM is there for the GPU to access in order to render the texture files etc, but if your GPU is fast enough, your video RAM would never fill up thus getting a card with lots of video RAM won't help you as your GPU would always be able to keep your video RAM free.
Basically I suggest getting a 6800GS and upgrading the system RAM as much as possible. That way your son can enjoy a much more responsive computer. Though he probably wouldn't be playing the game at full settings, he'll at least have a snappier computer as well as being able to play Oblivion on normal settings.
A personal opinion though, I'd rather save that few dollars you plan on upgrading the video card and RAM and put it towards a new computer. It sounds like it might be much, but upgrading 4+ year old hardware isn't going to last much longer with the upgrade.