I got the Classic Pack, and the DLC version of the 10mm pistol does more damage. But the "sturdy" name for the caravan shotgun might mean that it decays slower?
EDIT: Oh, VISUAL differences? I don't know about the shotgun, but the 10mm looks quite different.
The Sturdy Caravan Shotgun packs a punch. The Cowboy Repeater beats it in every way outside of close range, but if you play like a proper Shotgun Surgeon and run into close range you can instagib people in one blast to the face.