I don't know what the various makers use, but there is a lot of difference from brand to brand. Older Remington barrels are fairly soft. The newer 3" magnum barrels are much harder and thicker. Mossberg barrels are softer then Remington barrels, but much tougher. I don't do a lot of work on Winchester or Benelli barrels, but they seem fairly hard.
I am baseing my opinion on drilling close to a million holes in various barrels. After a while you can tell the quality of the steel by how it reacts while machining.
I'm sure that most of you don't remember the class action law suit against Dupont. The suit claimed that Remington made defective shotgun barrels. At the time, DuPont owned Remington. Dupont lost the suit and even though they claimed that there the barrels were safe, the steel was changed and the barrels were made thicker.
I will not work on the old 2 3/4" barrels. Of the thousands of barrels that I have worked on, with only 3 exceptions, the only ones that had problems were the old thin pre-law suit barrels.