I have only one experience with a stainless brush. It was 30+ years ago, used on a rifle. The rifle was a M700 Remington .30-06. The brush was brand new, and of a prominent brand, I don't remember which.
I had pushed the brush through the bore a few times from the breech when I noticed tiny slivers of what appeared to be steel accumulating on the clean newspaper I used to protect my table. Closer examination revealed similar slivers on the bristles of the brush. The slivers looked like remnants of fine steel wool.
I immediately suspected the stainless steel bristles were gouging my barrel. To my dismay my suspicion was confirmed when I found that the slivers were attracted to a magnet.
I have never used a stainless steel brush on any firearm since, nor will I do so. I strongly recommend against them.
Curl