Are shotguns portrayed realistically where in they have variable range depending on the load they're firing, or are they only close-range derp weapons in New Vegas?
Both 20 ga. and 12 ga. shotguns fire buckshot by default. The spread of the shotguns in F:NV is directly related to the barrel length. The single shotgun and hunting shotgun are pretty darn accurate (the latter is extremely accurate when equipped with the choke mod), but the sawed-off has terrible accuracy. The caravan shotgun, lever-action shotgun, and riot shotgun are all "in between" due to their moderate barrel lengths.
Firing slugs out of any shotgun will improve their accuracy in F:NV (an inherent property of the ammo type), but they are not rifles.