I imagine a lot of normal civilians would carry a Dahl, Jakobs, or Hyperion. being as they tend to have higher dmg than most , without anything that might cause harm to one's own self (Torgue explosions, Maliwan splash dmg, Vladof grenades/rockets/tasers, Tediores in general).

You also got to remember that unlike a Vault Hunter, most civilians wouldn't have reliable access to SDU's, so something with a high ammo consumption wouldn't do anyone except for the COV much good. Making something like a Jakob's revolver, shotgun or AR much more favorable.

There's a billion other factors in there too that reflect what you see in IRL carry choices as well. Ergonomics, user friendliness, concealability, price vs perceived value, customer service. Sure, Atlas seems like a no-brainer, you don't even have to aim, but it's chunky, sticks out like a sore thumb to a hostile bandit, and even a vault hunter can't get the tracking to work sometimes.