While steel type and hardness factors into it, the primary difference is that gunsmithing screwdrivers have hollow-ground tips. The contractor/handyman/household screwdrivers (Craftsman, etc.) are taper-ground. They're great screwdrivers around the house, but they are not suited to gunsmithing.
If you look at the profile of a hollow-ground screwdriver, the blade is the same width for 1/8 inch or so back from the tip, then flares out rapidly to the width of the shank. A taper-ground blade has a profile that tapers from the tip to the width of the shank.
Gun screws tend to have fairly narrow, deep slots, because they frequently get torqued more than typical houshold screws. Unlike taper-ground screwdrivers, a hollow-ground screwdriver tip will fill the entire slot of the screw and not try to "walk" out when you torque it.

Bottom line: Those buggered up screwheads you see on older guns come from using taper ground screwdrivers.