Not sure how trying to compare a pump and double as near equals in something like a fight can stand on its own without being somewhat selective in how its interpreted.
Talking about short stroking a pump, you can also fumble breaking a double open as mentioned previously which can be not opening enough, closing enough, or slipping the switch to break it open.
Dropping a shell when reloading a pump, by the time you start to have to reload a pump you all ready had 2 opportunities to drop shells with a double. Don’t have to top it off fully to be back in the fight either, if you only get one or two in then your no worse off then with the double. Probably also have some sort of pause and cover or concealment at this point with six shots all ready fired to offer more opportunity to reload unlike two quick shots.
Ease of use, pump you just pump firmly and pull the trigger until you need to reload where as the double you must break your shooting position and grip to use finer motor skills to break it open, pull out old rounds, move hand to fresh rounds, put them in the tubes, close, and resume firing position every 2 shots with the real benefit being the firing of two consecutive shots quickly (though with that thing called practice people can be hellishly fast with a pump).
Reliability, yeah if everything is done right with a double then its .something % less likely to have a malfunction then a pump.
Not to fully discredit the double but pumps will likely result in the better chance to make it through a fight with simpler and more gross motor skills, more shots before needing to pause (though both in theory have more than needed), etc.
If someone were to spend hundreds of hours with a double and not a single hour with a pump then there might be no advantage for that individual to use a pump since their proficiency with a double and alienation with a pump will likely win out.