For decades, people have been told to buy a pump because semi autos were not reliable. Times have changed, just as once revolvers were king in law enforcement, and for good reason. Now pistols are considered as reliable as revolvers or even more reliable. It depends on the pistol, of course, and the same goes for shotguns. The Remington 870 is notorious for operator-caused malfunctions. The 870 works well if the operator knows how to use it under stress, but a semi auto provides fewer chances to screw things up. Just pull the trigger. On the other hand, a negligent discharge with a pump will result in only one round going off, but with a self-loader, people have actually unintentionally shot others or even themselves two or three times before gaining control of their stupidity and taking their finger off the trigger. The recoil startles them and in their attempt to hold onto the gun, they pull the trigger again. That cannot happen with a pump. It's not really that important, since the operator must be responsible enough to touch a gun in the first place, no matter what type it is, but it's worth mentioning.
Today there is really no reason to buy a pump, except for the lower price. I have a pump that's been in my possession for decades, but if I were going to buy a home defense shotgun today, it would be the best semi auto I could find. Revolvers are a different matter. I still love them, though I carry Glocks and 1911s, too. When hunting, it's always a Smith .44 mag revolver on my hip.