The Marines don't issue 870s. They have a fancy new Benelli autoloader. The guards at the gate here usually have one of those, sometimes they have an M4 variant, sometimes a flat top M16. The old A2s don't usually end up overseas. (Army is mostly M4s except for DMRs.) When the Federal Police are standing guard, they have M4s. I haven't seen a pump shotgun save in the hands of MAs on a Navy warship.
Guarding prisoners usually nets a shotgun. Otherwise standard guard duty means taking the standard issue weapon along.
Rifles and carbines are somewhat better for the job since one might have to shoot at vehicles running barricades. Not that the 5.56mm is ideal for that, but works better than a shotgun with buckshot or non lethal (rubber) rounds. Slugs aren't usually encountered.
MPs carry the Benellis in the trunks of their squad cars on base and presumably deploy with them. Regular units don't usually draw them, though SOC (spec ops capable) units could of course get them if they were needed for the mission.