Bronze brushes are softer than your steel barrel so you are ok if you clean from the breech and don't overdo it. Nylon is actually somewhat abrasive, but is useful when using copper removal solvents that would attack a bronze brush. Stainless brushes are a BAD idea IMO.

It's easier to ruin your bore with overcleaning than it is to wear it out shooting. If you have a semiauto or lever gun that you can't clean from the rear, use one of the conical bore guides so as not to nick your crown.