Having owned both, and used both considerably, I a Remington 870 man. My 1958 870, which I bought some 30 years ago, works just fine and still does anything needed. The first gun I bought new was a Moss 500 and I proceeded to shot it into the ground. When the cost of the needed repair parts cost as much as it cost to buy, I sold it. I now have at least three 870s, which I will never be able to wear out no matter how often I shot them, and my grandchildren should be able to hand them down to their children too.
We had a 870 that had been lost in a hog barn for over a year, buried in pig doo, and when we cleaned it up (we boiled the shot out of it) it was still 99% usable! The extractor was in poor shape (very corroded, still worked however), no stock wood (at all), the extractor spring was toast (amazingly, the rest of the springs still worked, but we replaced them all anyway as some were obviously in bad shape), but except for the spring, everything worked!
Go look at IPSC shooters, serious duck hunters, trap shooters, you know, people who actually USE their shotguns and see how many of them use a Mossberg 500. Well I lived on the Mississippi for years and I never saw a Moss 500 in the duck blinds, although I suppose it could happen. I don't know of any trap shooters who use a 500 either. I saw plenty of Rem 870s in both places however.