Stainless pros: Easier to machine, so your gunsmith will like it and it is less destructive to reamers. Less prone to corrosion, esthetics either way. All the uppity-up swave and de-boner F-Class guys like stainless, and their mountain top gurus claim better accuracy. (Buhllschitt)
Cons: Unable to blue or parkerize. Must leave alone or paint. Not as safe in extreme cold weather; some companies will only produce SS barrels in larger diameters due to controversy over their suitability for extreme cold weatehr use and their safety with hge cartridges in smaller diameters (um, aren't the breech diamters the same? Hmmm.)
Chromoly Pros: Cheaper, safer in extremely cold temps, available in lighter contours. Can be blued or parkerized.
Cons: Rust, machinability.
Myths: CM barrels are less accurate or foul more.