One is the tang placement of the safety switch. It's not necessary to change the position of the shotgun from the firing position to switch it on or off.
The other is the loading gate. In the Remington there's a piece of metal that can catch fingers or gloves. To load the Mossberg you simply drop the shell in place and shove it forward making reloading much simpler.
The 500/590 series also comes drilled and tapped from the factory. The 870 requires gunsmithing to add optics.
For a hunting shotgun I'd go with the 870. For a defense weapon the 500/590 is superior IMO.
I have a Mossberg 590 loaded with BB shot in the hall closet, and a slug-barreled 870 in my bedroom. I also have several other 870s in the gun safe. I would trust any of them in an emergency. My favorite hunting shotgun is a Beretta Urika.
For me it has to do a lot with the stock / grip.
Using a standard stock, the Mossy safety is located better, but with a pistol grip you now have to move the trigger hand around to reach it (at least I did).
The Remington (or Winchester) with the safety at the trigger guard is better suited for use with a pistol grip, but not so much if you use the standard stocks.
So I have standard stocks on my M500A, pistol grip on my R870.