You do not mention what brand shotguns you shoot. I will assume that they are newer shotguns that were designed to withstand the effects of shooting steel shot. You also do not mention if you are shooting steel, tungsten, or bismuth shot.
I will guarantee you that if you shoot steel shot in an older shotgun, that was never intended to shoot anything but lead, it will damage the barrel.
Not long after the feds introduced the "Non Toxic Shot" restrictions for waterfowl hunting, a friend of mine blew the winchoke completely out of his Winchester 1300 pump gun. Because steel is much harder than lead, it does not compress when it encounters the choke at the end of the barrel. It ends up creating a bulge right in front of the choke (or blowing the choke clean off!) and ruining what is often a very valuable firearm.
Many years ago, I asked a wildlife biologist if he had ever actually seen a duck or goose that had died from ingesting lead shot while feeding. He admitted that he hadn't, but he assured me that the "threat" was legitimate. I then asked him how many birds he had found that were crippled by the much less efficient steel shot, and later died without being recovered. He didn't have an answer!
I will not shoot steel shot through any of my guns because of the unacceptable level of cripples it causes, and I refuse to ruin a fine old Browning just to be politically correct.