I have three types of shotguns: double-barrel, pump and semi.
My experiences are pretty limited. However, I would keep the pump over the other two if I could only have 1 shotgun.
In my experience a semi-auto shotgun, as a category, is not the best for a 1 shotgun, end of times, scenario.
My experience has shown that you have to spend the time to find the loads that the shotgun likes. I don't mean in terms of patterning, but in terms of loading and ejecting.
For example, my semi won't cycle low power loads under 1250fps and under 1oz on a reliable basis. It fails to eject them, and then tries to load. Jams are only fun on toast or in the garage.
In my experience, a pump can handle 2.5 dram loads all the way up to my 'monster' 3.5" magnum rounds. And all without doing anything more than wincing at the pain.
My semi can handle hotter rounds, after changing a gas bushing. But the low stuff jams it.
I know that others have VERY different results. I know that others have MUCH more extensive experience. I know others say 'well, just use the rounds the semi was designed for'.
However, if I can only have 1 shotgun, I want it to chamber/fire/extract/load every available round of the gauge and shell length that it was designed for.
A pump does that without hesitation. Semi's may have a narrow range of load options that they are reliable with.
Now, I also understand the 'right tool for the right job' approach, and there are better models for each application for a shotgun. That is why I have SxS, O/U, and Semi. Yet, a pump allows someone to accomplish almost any application.
Kind of like a Honda Accord can do almost anything that a person needs from a car [not a truck], like getting to work, taking 4 people to dinner/movies, bringing home groceries/mall shopping, long trips to national parks, fun drives in the mountains/along coast. However, there are car models that are better for every application. Most people can't afford multiple cars.
I know, shotguns are not cars. But, some people can't afford multiple shotguns either.
I am sure that more reliable semi-auto shotguns can be found than mine [S&W 1012, from Turkey, @ 2005], but I am also confident that they cost more than a $400 Rem 870 or Mossy 500.
Again, I'd keep my 870 over the others if I could only have one, but I'd miss the others.