For shooting pests? Get whichever one you can find cheaper.
This.
The Mossberg 500s have alloy receivers, are as common as dirt, and are unlikely to be family heirlooms, but they are proven tools that sell in a lower price niche. If I was going to buy a pump action .410 barn gun, I'd buy a Mossberg. If I was going to buy a pump action .410 to shoot skeet, I'd pay extra for the fit and finish of the Remington 870.
I've never owned a Mossberg 500 in .410, but have owned them in 20, 16, and 12 gauge. My 20 gauge rifled bore slug gun is more accurate than either of the Remington 870s with rifled bore barrels.
