Bronze, brass, and soft iron will all work quite well for cannon barrels as long as they're thick enough and the powder burns relatively slowly. It's the quality of the gunpowder that would make the big difference here; for example the English naval fleets once had a serious problem with cannons exploding because the supplied gunpowder was too finely-grained and thus burned too quickly, causing the barrels to rupture.

Edit: In any case, Roman metallurgy wasn't that far behind metallurgy in the 13th/14th centuries when cannon arrived on the battlefield. Also, as a bit of trivia, cannon were instrumental in the Turks' conquest of Constantinople, the last continuous remnant of the Roman empire.