^ Shooting bullets through your barrel will wear it down quicker than a bronze brush will sir.
Kind of depends on what you're shooting, how much you shoot, and how much you scrub, doesn't it?
Lead is pretty soft, so is copper. Bronze is mostly copper and a little tin and much harder than copper alone. If you're shooting copper-clad lead rounds, I think that makes the round shot a bit HARDER than lead alone, but softer than the bronze brush. Some folks may be shooting steel -- ala the cheap imported ammo -- and that's arguably much harder than a bronze brush.
Using bronze brushes CAN accelerate wear -- but if done judiciously, it probably won't matter much; done heavily and regularly, it could make a difference.