Brushes will not harm your barrels.
Some solvents with ammonia,will damage your bore,if you leave them in the bore for prolonged periods.
Most rods will never damage your bore if used correctly. I use 1 pc stainless steel rods on all of my rifles,but I always clean from the chamber end. If you have to clean from the muzzle end,you need to take care not to damage the rifling at the crown of the barrel.
Aluminum or Brass rods are softer than the steel in your barrel,and cannot damage the rifling.You might shave off small pieces of the rod inside the bore,but when you run patches thru the bore,they should be caught in the patches.
Bore Snakes are a great tool to have in the field,if you need to clear the bore of unwanted debris - dirt,water,snow. But,I would never consider them as a bore cleaning tool,after the first pass,your just dragging a dirty rag through your bore.Your not cleaning it!
I really like the foam cleaners,but I still use a brush on the bore after the foam has worked on the bore for 15-20 minutes,then patch out the bore.If it's still dirty,repeat the process until the barrel is completely clean,then run an oiled patch thru the bore.
Texas State Rifle Association
North American Hunting Club