From Fire-Arms Manufacture 1880. U.S. Department of Interior, Census Office
The earliest use of decarbonized steel or gun-barrels is generally credited to the Remingtons, who made steel barrels for North & Savage, of Middletown, Connecticut, and for the Ames Manufacturing company, of Chicopee, Massachusetts, as early as 1846. It is also stated that some time about 1848 Thomas Warner, a the Whitneyville works, incurred so much loss in the skelp-welding of iron barrels that he voluntarily substituted steel drilled barrels in his contract, making them of decarbonized steel, which was believed by him to be a a novel expedient. The use of soft cast-steel was begun at Harper's Ferry about 1849. After 1873, all small-arms barrels turned out at the national armory at Springfield were made of decarbonized steel (a barrel of which will endure twice as heavy a charge as a wrought-iron barrel), Bessemer steel being used until 1878, and afterward Siemens-Martin steel.
What is missing is the next sentence, which I did not post at the time:
The loss on barrels welded from the skelp sometimes ranged as high as from 10 per cent to upward of 20 per cent on account of imperfections in the wrought iron and in welding. The loss on drilled and rolled steel barrels is only a fraction of 1 percent, and in some large contracts has been within one-tenth of 1 percent.
In proving the (pistol) barrels ... Although only a small percentage (for decarbonized steel barrels about one-sixth of 1 percent) is burst in the proving...
So the advantage of decarbonized steel was the lack of imperfections.
Back in 2005 there was a long discussion about the strength of various steels. Geno provided these figures from a 1905 work by Prof Buturlin.
Steel Type Max (lbs/sq in)
Damascus -------------- 31,291 to 52,626
Typical 1905 Steel --- 64,000
Winchester Steel ----- 39,400
Winchester Nickel --- 88,600
Krupp Special --------- 85,340
Krupp 5 M ------------- 92,450
Bohler Antinit ------ 116,630
Pete