Although the 8800 and your x600 both have 256MB of memory, the memory on the 8800 GT is faster, newer technology, as is the 8800 GT's core.
The 8800 GT is at least twelve times as powerful as your x600--you'll see a TON of improvement regardless of whether you go with the 256MB or 512MB version of the 8800 GT.
The 256MB version is more than adequate for casual gaming, which seems to be what you need it for. And 100$ after rebate is a great deal.