I've had/have both. I had a Remington 870 Wingmaster years ago, when the Wingmaster had nicer receiver and wood. I bought it used, shot trap with it almost every Thursday night for just over 5 years, 200 rounds every week, plus the occasional turkey shoot, skeet and sporting clays trip, and of course hunting. Put over 50k rounds thru that gun and it NEVER failed me. I bought my wife a youth model 870 express in 20 gauge, with a short 20 inch barrel. I LOVED that thing, and ended up hunting with that for years and left the old heavy 12 gauge Wingmaster at home.
That being said, there were things about the 870 that always bugged the bejesus out of me. First, was the slide release, which always seemed to be in the wrong place, I think Remington put it in the wrong place and Mossberg got it right. I also hate the location of the 870 safety which requires I move my finger away from the trigger to move the safety. My Mossberg safety can be reached with my trigger finger on the trigger guard, ready to move into position for the shot. Lastly, I really don't like the loading gate on the bottom of the 870. Any hunter who's hunted alot in winter will tell you that damn thing likes to snag your glove tip.
So, I moved years ago, sold all the guns before I moved. Got to the new home, got an itch for a shotgun again, looked around, and found a really nice Mossberg 500 in a pawnshop for $200. Over a couple of years, I found 3 more barrels for it, each $40 or less. I replaced the cheap plastic safety with a very nice metal Vang Comp Big Safety. And I removed the old Mossberg wood stock and handguard and replaced them with the Magpul furniture instead. Yes, the Mossberg has been as reliable so far as the 870, though I've only put a couple thousand rounds thru it in 15 years, not nearly the volume the 870 saw. I don't see any difference in one gun being harder or easier to clean than the other.
Visually, I think the Remington is a nicer looking gun, and to be honest with you, even though the Remington weighs more do to its steel receiver, I find I shoot better with the Remington than the Mossberg. Now, that may be due to the years and years of using one, muscle memory and all that, but it is what it is. I shoot (trap, skeet, clays) better with the 870. My Mossberg controls are all in the right place, I intuitively find them. I have to go hunting around for the Remington controls.
Is one better than the other? Probably not at this point. Its as old an argument as Ford-vs-Chevy and "which (motor oil/beer) is better"? You can't go wrong with either, there's a gazillion parts available for both, barrels are everywhere, chokes are everywhere, it comes down to which one feels better in your hands, which one shoulders naturally. Gunsmiths are familiar with both, pawnshops are loaded with both. Can't decide? Buy both, shoot them for a year or two, then sell the one that you think you can live without. It's not a Benelli, you can buy both without going broke.