Overall the combination of 5% faster core clock and 768 MB of additional memory can yield a performance improvement of about 10% when comparing Sapphire's HD 3850 1 GB to the HD 3850 with 256 MB. In my opinion this is not worth the price premium of $50. The gains get progressively bigger the higher your resolution and the more eye candy you have turned on. However, you also have to consider that at some point the raw GPU power of the card will reach a limit where more memory will not help.
Overclocking this card was a pleasant surprise with overclocks of 13% (core) and 17% (memory) over the card's stock values. This should give you a nice performance boost getting the card to surpass the stock HD 3870. Even though the single slot cooler seems to be quite basic it does a good job at keeping the card cool, even during overclocking. Unfortunately the fan control is not ideal because the card tends to jump between fan speeds, especially when you are in 2D. Also the fan in general is pretty noisy in 2D and 3D, I would have prefered higher temperatures for a quieter card.
Last but not least having a graphics card with 1 GB of memory might give you a serious bragging rights advantage over all the poor peons with only 128/256 or 512 MB. There is also a chance that game developers might start taking real advantage of 1 GB memory, but I don't see that happening before 2009 on a larger scale. Overall, unless you have a specific reason to need 1024 MB of video memory I would recommend going with a cheaper 256 MB or 512 MB HD 3850.