ah, but Mikey is only partly correct! A generation ago, stainless gun frames/slides/bolts used to have a bad reputation being "soft" for needing special anti-galling lubricants. That has been fixed with newer alloy developments.
Modern blued rifle barrels are usually 4130 chrome-molybdenum steel alloys, and as such can be "blued" (black oxided). It's an established technology, since alloy steels became common in the 1920's. Before that, low-carbon steels and nickel steel alloys were the standard barrel "ordnance steel".
"Stainless steel" contains much higher chromium content, among other trace elements, and as used in gun barrels, is much more resistant to flame-cutting and powder/primer erosion than blued steels. It is much more durable, and can give close to double the barrel accuracy life of a comparable carbon/moly steel.
Competiive high-power and benchrest shooters prefer them for those reasons. It's a newer technology, established only in the last couple of generations and perfected by barrel makers.
As for stainless being "stiffer" and more accurate, I've not heard or seen that in metellurgy studies.
Early stainless barrels could not be blued, and gun makers had to copper-plate or paint (yuck!) them to make barrels dark. Space-age chemical treatments now make it possible to "blue" stainless barrels, but it's an expensive treatment.