More important then barrel material is rifling design. Generally the 3 groove rifled barrels will have the longest throat life because there is more steel in the origins of the rifling compared to the 4, 5 and 6 groove designs.
That said, again, it all depends on how you shoot the rifle.
For all the 257 STWs I have built, ever one has been fitted with a Lilja 3 groove barrel, 90% of which have been stainless steel.
The 257 STW is about as hard as it gets on throats. Why not take every step to get the longest throat life possible. To me that would mean a stainless 3 groove barrel.
There have been several tests that showed that there was no difference between stainless and chrome moly barrels reguarding barrel life, there have been several times as many more that say there is anywhere from 10% to 25% longer throat life with stainless barrels.
I have yet to see a study that said chrome moly barrels offered longer barrel life then stainless so for a chambering like the 257 STW, why not go with the percentages and get a stainless barrel.
If you like a blackened barrel you can always teflon coat it as well.
Kirby Allen(50)