A sideline I have is a local gun cleaning business, and I take in a couple of dozen 870s each year to clean, probably half as many Mossberg 500/590s and a sprinkling of 1200 Winchesters. These are usually company guns that are used in a harsh environment and see little love, so if a gun is going to fail, these are the circumstances in which it will. My comments will be directed to the 870s and 500/590s.
Both Remington and Mossberg guns are good quality and reliable. Both Remington and Mossberg guns have a wide assortment of after market accessories available for them. That said, my preference is for the Mossberg line. My preference is the 500/590 Mossberg which can be had in 18" length.
Common maladies for the 870 include broken ejectors, lost extractors, and unpinned shell stops which tie up the actions. The Mossbergs have ejectors that are held by a screw and are easily replaced, the Remington ejector is a thin metal strip riveted in place, and is easily broken when the barrel is jammed into the receiver without taking care to index the ejector, and it requires a gunsmith to repair. Mossberg shell stops sit loosely in groves in the receiver, and are absolutely reliable. The Remington shell stops are staked in shallow recesses, and should those stakes fail, the loose shell stops tie up the gun. The 870 relies on a single extractor, the Mossberg has two. I prefer a magazine that is open at both ends, and for this reason I think the 870 and the 590 have the advantage over the 500. That said, a 500 magazine tube can be threaded for cleaning, which allows the removal of the follower and spring. The factory metal followers for the Mossbergs should be replaced with nylon followers if the gun is exposed to wet conditions.
In shooting both guns, the action release for the 870 is forward of the trigger guard requiring the shooter to break his firing grip to reach it, where the 500/590 action release is conveniently located behind the trigger guard. The 870 uses a cross bolt safety behind the trigger guard, where the tang safety of the 500/590 is again more conveniently located. Triggers between both brands are acceptable. Given a chance to smooth up, both actions can become fairly slick, where with a cocked gun, and the action release depressed, a light bump on the butt will fully open the action. I prefer the elevator of the Mossberg compared to the "flicking" action of the Remington, but both are fully reliable. Both allow easy indexing of the shell from the face of the t rigger guard to the magazine when loading at the shoulder. Both guns can be easily unloaded by depressing the shell stops allowing the shells to exit the magazine.
