Stronger?
Strong is good to keep the barrel from bulging. Ductile is necessary to keep the thing from shattering when something goes wrong.
Just for fun, here is quote from an 1888 report of the Birmingham Proof House:
"The endurance of a barrel appears to depend upon a moderately high elastic limit (which prevents bulging) and a fair margin between the elastic limit and the breaking strain (which prevents bursting). If the composition of the metal and the method of manufacture are such as to yield a low elastic limit, the barrel is too soft and bulges easily; while, if the elastic limit be unduly raised in proportion to the ultimate tenacity, the metal is deficient in ductility, and, being thus brittle, the barrel bursts"
The original paper is from Experts on Guns and Shooting, p 264, Longon, 1900, reprinted by The Buckskin Press, Big Timber Montana, 1981.