SwampCollie, my system crashed at work and Sabotloader beat me to it.
Just to be clear, unless you have some kind of after market application, TC does not make any ML "stainless with weather shield." It is either actual stainless steel with no coating, or it is a standard barrel with weather shield coating on the exterior (meaning, no coating in the bore). I called TC to confirm this. I say this because I know of a few retailers that refer to the Weathershield treated Omega (Z5) and Triumph as “stainless steel muzzleloaders.”
Regarding the corrosion resistance of blued versus stainless, I was out yesterday with my Omega X7 (stainless) for about four hours in constant rain. Forgot to put a dry rag in the car and did not have a chance to really clean it until the kids were in bed, many hours later. No sign of any corrosion. If I had a blued barrel I would have found time to clean it sooner. The point is not that stainless is impervious to any rust or corrosion, just that it is more resistant than regular carbon steel. I honestly thought everyone knew that.