In a muzzleloader, the only material advantage to a stainless barrel in my experience is that it's easier to tell if it's clean than a blued one is.
I've never had any rust problems with blue finishes or stainless finishes. And stainless will absolutely rust if you don't protect it. But that comes to the treatment of the metal. I don't "oil" my barrels on the exterior at all. I use Outer's Sheath protectant or I use a good automotive car wax and give the gun a couple of light coats. Sheath passed a 7 day saltwater spray test, that's good enough for me. I hunt in the rain, storms, downpours, and snow storms with nary a problem. There are other products that are offer similar protection. I'll tell you that the Rusty Duck protectants SUCK, don't waste your money on it.
I prefer a matte blue or black finish for looks. Teflon, parkerizing, expoxy, etc. Stainless does look good with laminates. In my mind, I think that a stainless finish is probably easier for animals to see if you are moving around, but if the animal is close enough to see it, then I should be watching it through the scope! The only stainless gun I have right now is a new Omega, and it's only stainless for the reason in the first line above. All other guns I have are either blued or parkerized. There's a reason that gun's have been blued for the last couple of hundred years: it's economical to do and it WORKS.
I actually had a gunsmith talk me out of having a new Encore and couple of barrels parkerized. When he asked me why, I told him that I wanted something that offers more than "just the blue". He told me to save my money, use a treatment on the blue, buy another barrel or scope with the money, and when the finish on the gun is worn enough, to call his number and maybe his grand kids will be running the shop and they'll refinish it for me.
That was enough to convince me that blued is fine.
