Even 1280MB won't be enough for GTA IV and BF3. You need 2GB these days. 1GB is a minimum.
I'd probably go for a 6950: http://www.newegg.com/Product/Product.aspx?Item=N82E16814150523
Bonus points for finding a reference card that you can unlock the shaders on.
It's better to buy now and be prepared than to save some money now and be lacking in playability when you want it.
At 1920 x 1080 i doubt he is actually seeing a buffer overload.
You just don't have enough grunt. Your motherboard chipset is budget, and your CPU can be overclocked. Buy another card and crossfire. Its not VRAM.