Stainless steel is softer than carbon steel. Should not be any issue.
This statement may or may not be true. It all depends upon the alloy used, and the heat treating used. Stainless steel can be hard and brittle or soft and ductile, and the same can be said for carbon steel.
I've used a few Tornado brushes and they did a good job without scratching or damaging any barrel I scrubbed with them. The Tornado brushes are made in both stainless steel and bronze versions, but the ones I used were stainless. And the vast majority of shotgun barrels I clean are old vintage fluid steel or Damascus barrels. They have been in use for many years, and if they were damaging barrels, we would have heard it by now. One claimed advantage was that the looped construction left no sharp exposed ends as is found on conventional bristle brushes. But that also means they may bridge across any minor pitting found in old barrels, so a conventional bronze brush could be better for getting into recesses like that. And wrapping a bronze bristle brush with some steel wool does help them clean more aggressively. It also extends the useful life of old worn out brushes.
