You need to be more specific.
256mb of ram on a card doesn't change much (in a negative way) IF the speed and timing is the same. 256mb on a system would be a factor for some types of applications but not favour one or the other.
But at stock speeds the R9600XT would beat the R9600UE every time because of the core speed differences, not the memory differences. Yes the R9600XTs initially came out with much slower memory than the older R9600pros, but the Ultimate Edition was no guarantee of fast memory. The Sapphires in particular had a missmash of memory types (7 different speed/mfr combos I've seen so far).
Which is a better card depends on the precise specifications of the cards, but which one will perform better at stock speed out of the box, the XT, every time because it's 500/300 vs 400/300.
Even the Best Sapphire R9600Pro Fireblade edition, only guarantees an overclock to 330mhz, but out of the box it's still 400/300.
However there is no way of telling which would overclock the best without true specs. But based on the multitude of reviews I've read, the Ultimate edition usually comes with 3ns or worse memory, so there would likely only be a tiny bit more overhead on the memory, and that would usually be versus the INITIAL R9600XTs which still enjoy far greater core overhead. So you may get to the point where a 550/315 card would lose to a 450/320 card, but that in and of itself would be rare.
The Simple answer is that the R9600XT would beat the R9600P-UE 99.44% of the time under stock configuration, whether it's 128mb or 256mb.
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