I personally don't like pump action shotguns for HD just because, if you aren't well trained with it, you can easily make mistakes.
Namely the pumping between rounds. I have taken my friends to go shooting and, despite me mentioning that people always forget to pump their first times using the gun, they made the same mistake.
I imagine it has to do with all the adrenaline going through them that they focus more on the shot than on what to do after. I feel that it would be similar in a HD situation.
Obviously you should train with your HD weapon of choice but for people that only have their firearm for self defense, practicing shooting is probably not something they do often and they may forget some of their training.
That's why i prefer stuff that is a bit "simpler" such as revolvers(pull trigger and aim with a reduced chance to jam compared to semi-autos), Semi autos (also just pull the trigger once there's one in the chamber and even though they jam more than revolvers, its not very common so long as it is held correctly), or semi auto long guns such as ARs.
Pump action shot guns, single action only revolvers, and bolt action guns are what i would advise against for HD.