They both will get the job done equally the same. The nice thing about the Mossberg is you get 3 choke tubes (imp cyl, mod, full), while you only getthe mod with the Remington. The Mossberg also has real blued steel, but it does have a plastic trigger gard.
The Remington feels like a better made gun, and not something that was thrown together from parts laying around. I have a 500 12 gauge, my buddy has one in 20 gauge, and another friend has the 870. I will be getting an 870 soon.
15 or so years ago when I bought my 870, I liked the way it felt much more than the Mossberg. The Mossberg seemed "sloppy", while the 870 felt "tight". Things have likely changed over the years, though.
The ole' 870 is still kicking just fine after all these years, and has taken just about every type of game available in PA (no bear or coyote, although it could, given the opportunity!)
I bought my 500 about 10 years ago. I really wanted the 870, but Mossberg had a much better combo package at a much better price than what remington had at the time.
My 500 has taked tree rats, rabbits, deer and coyote. The gun works flawlessly. Like Larry said though...it feels sloppy. Another thing that bothers me, the finish where you hold it has turned a milky white.
I prefere the 870 express....Wife has the mossburg only because she hunts less and probably not as hard on the equipment as I am. Both are accurate and should last. I prefer the 870 but have been hunting with it for a long time now. I just like the availablility for aftermarket barrels, stocks, camo covers and such. I am sure the mossberg has them as well.