George,
Hi!
Ironsraven has provided a very good summary comparison.
On a more subjective note, I have used and owned both. The Mossberg 500 was my first real shotgun; the Remington 870 was my second (acquired as a steal of a deal for a 15 yo a year and a half later). I much preferred the looks and feel of the Remington. I traded away the Mossberg ; I still have the Remington 40 years later. The last 2 guns I bought were Remington 870 Express model for my sons.
Let me to give you an idea of the reliability of a good pump gun: I reload my own ammo. Occasionally some of it will not readily chamber in the mostly gas operated semi-automatics that I tend to shoot nowadays. When I have accumulated enough of those rejects, I shoot a round of skeet with my Rem. 870 police model and the semi-automatics' rejects. Nearly all of the ammo, which was rejected by a semi-auto for sizing reasons can be made to function through my Rem 870. And the functioning is adequated for skeet shooting purposes. Guess what I rely on for defensive purposes. Incidentally, I have no reason to believe that the Mossberg 500 would be any less reliable than the Rem. 870 for defensive purposes. My trade of the M500 was due only for reasons of esthetics and economics for a poor farm boy.
Good luck,
John