Both barrels are correct. more swamped earlier, and in flint, and a lot less with he advent of percussion, after around 1815 or there a bouts. Today's swamped barrels are more profiled than those of that time period. Jerry Nobles books have many examples of both in his four volumes. The real constant is that the locks are of English import hardware styles, as the Smiths in the south were mostly of English, and Scottish decent. Another aspect of these barrels is their length. a 42" one would be considered short, and 45" to 54" would be more common.
Bill