Doing some research of my own. Here is what I found from Rage 3D.com
Product : Sapphire Radeon 9600 Atlantis 256MB
Company : Sapphire
Author : Ratchet
Editor : Ichneumon
Date : October 30th, 2003
Conclusion
Straight to the point, the only instance where a 256mb frame-buffer would show any current advantages is when running in a high-resolution and high Anti-Aliasing setting. Putting it on a card that can't possibly handle that combination is nothing more than a marketing gimmick.
The reason why we see 256mb on a lot of the low-end and low-mid range cards is simply because companies can get away with using slow and cheap TSOP (Thin Small Outline Package) ram instead of the more expensive and faster BGA (Ball Grid Array) ram normally seen on faster cards. It's all pure marketing of course, it doesn't take a PhD to know that "256mb of DDR Memory" looks very good on the box when more expensive cards only sport 128MB. If the low-end cards had enough pop to take advantage of 256MB of memory then I'd be singing a different tune, but low-end cards, by their very definition, don't have near enough horsepower to run at those demanding settings. It's a checkbox feature to entice consumers who don't know any better, plain and simple. Obviously though, with full support for DX9 and all the technical features of it's high end Radeon 9800 cousin (6x RGMSAA, 16x AF, PS2.0+, etc) the Radeon 9600 256MB isn't as low-end as, say, a DX8.1 generation Radeon 9000 or 9200, but as you've seen in this review it still doesn't have the power to make using combinations of high-resolution and any level of decent Anti-Aliasing practical.
If you find yourself trying to decide between a 9600 with 128mb and a 9600 with 256mb, save yourself the $20 and get the 128mb version.
I have an Athlon 1800+ with 640MB SDRAM. I plan on playing Unreal and Half life.
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