I have no experience with the Saiga, but of the other two, I would prefer the mossberg. This is largely because the safety is more ambidextrous (I shoot lefty) and it's easier to tell at a glance if it's on FIRE or SAFE.
Also, the 870 has a lever where you load the shells in the magazine, the 500 does not. Obviously, many many people have used 870s effectively with that lever, and it is likely a non-issue provided a person practices enough, but it does add a minor obstacle to reloading that is not an issue on the 500. Not that people wear gloves inside their homes much, but there have been times when I've been hunting when the thumb of my glove snagged on that lever after loading a shell.
If you're talking about 500 vs 870 field models (and not tactical models) the 500 has 6-shot capacity vs the 870's 5-shot capacity.
As semi-autos have gotten more and more reliable, I really think something like a mossberg 930 may be the way to go. It's gotten to the point that human error (such as short-shucking) with a pump is probably more likely than failure in a semi-auto.
Also, the 870 has a lever where you load the shells in the magazine, the 500 does not. Obviously, many many people have used 870s effectively with that lever, and it is likely a non-issue provided a person practices enough, but it does add a minor obstacle to reloading that is not an issue on the 500. Not that people wear gloves inside their homes much, but there have been times when I've been hunting when the thumb of my glove snagged on that lever after loading a shell.
If you're talking about 500 vs 870 field models (and not tactical models) the 500 has 6-shot capacity vs the 870's 5-shot capacity.
As semi-autos have gotten more and more reliable, I really think something like a mossberg 930 may be the way to go. It's gotten to the point that human error (such as short-shucking) with a pump is probably more likely than failure in a semi-auto.