Of course, you could just make this simple and own both.
The Mossberg M590 was what was thee standard issue shotgun when I first went into the Marines back in 1988. The Remington 870 is in the same dress when I first came back into the USAFR back in 2004.
Now the Mossberg I think has a better safety location but the plastic button is breakage prone and I swap mine out with a metal version. They are also easier to work on and in some ways are more prone to longer life than the 870. I say this because when I was at Hurlburt Field, we had 10 old 870 shotguns that were some EARLY 870 shotguns! The problem was that the shell catches were replaced so many times over the years that there was very little metal on the receiver left available for future restaking jobs if the catches needed to be replaced. Same goes for an ejector. Just how does a user replace this? It ain't easy and generally requires a trip back to the factory. The Mossberg doesn't have these problems. Another thing I like about the Mossberg is the lifter rides against the bolt. If a shell jumps the catches, the round falls out on the ground. In a Remington, a shell winds up on the lifter. If you have a newer Remington with the flex tab, it's not a big deal. With older guns, you have to take the gun apart or cut a slot in the lifter so you can run the shell back into the magazine tube with a knife blade. I have one 870 that I modified in this manner and it does work but like I said, it's not even an issue with the Mossberg.
Now the Remington does have a more solid feel and not nearly as "rattley" as the Mossberg. There are also scads of aftermarket parts for the 870 as well for the guys that have to modify them. The Mossberg is no slouch in this area as well, but the Remington still has more offerings. If you want to use a pistol grip design, the safety button of the 870 is far more friendly than the tang mounted safety of the Mossberg.
Really, you aren't going to go wrong with either one. Both are reliable, rugged and combat tested over the years. Just go ahead and get both, I did and am very happy with both designs....along with an Ithaca 37, Winchester Defender, and even a Norchester 1897 trench gun if you want a few more options to think about.