I thought it was gospel that a person who was used to his pump shotgun could cycle it faster than most or all autoloaders cycle. I don't actually know from experience.
I regard a clean autoloader, like my Browning Auto-5, as more reliable than a pump in my hands. That's because I don't play with shotguns a lot, and I recognize my limitations. There are plenty of ways to get a pump to jam through operator error, and I'm not so egotistical that I'll rule that out. I have never had a failure with my Auto-5. Also, the Auto-5 can be reloaded without taking it out of the ready-to-fire state. This is probably true of some or most pumps, but I don't really know, not having any interest in pumps.
It seems obvious to me that a good pump is a slightly superior weapon for the person who will be playing (shooting) with it regularly, and a good autoloader is noticeably superior for the person who hasn't and won't.