Ford or Chevy? Blondes or brunetts? Either one is going to work and you're not going to go wrong with either one. Owning both makes as well as working on them, here's a few things though I have noticed.
The Remington tends to be smoother out of the box than the Mossberg however, the Mossberg will smooth out over time and use...but both pale in comparison to the Ithaca M-37.
The Remington has a safety that doesn't break like the plastic Mossberg variety (although that is replaceable at a very reasonable cost) although the Mossberg is more ambidextrious in its design.
The Remington's steel receiver in theory is stronger than the alloy receiver of the Mossberg but then I've seen alunimum lower and upper receiver on M-16s on the firing line that have been around since the early 60s and are still in constant use without any problems as well as I've never seen a worn out Mossberg receiver...and alunimum doesn't rust either.
The Mossberg tends to rattle a little more than the Remington but it has a slide release that you can depress without breaking your grip or sprouting an E.T. finger.
The Remington has more accessories available for it although Mossberg isn't too far behind. Yeaahh!!! Mall-ninja guns for everybody!
The Mossberg has a shell lifter that rides against the bolt so a shell jumping the shell stop simply falls out the gun where a shell on the lifter with a closed bolt of an 870 can tie up the gun. A cure for this though is to either cut a slot in the lifter like I did with mine so when it happens, a knife blade can shove the shell back into the magazine tube. Another cure that is better but more expensive is to replace the lifter and bolt carrier with the flex-tab conversion.
The Remignton can add an extended magazine tube very easily where the Mossberg also requires a barrel change as well. On the other hand, the Mossberg tube is one seamless piece with no butting surface that increase the chance of hanging up a shell or follower.
The Remington is the favorite with law enforcement with a few Mossbergs also serving in the law enforcement field.
The Mossberg is the favorite with the military with a few Remingtons also serving in the military field.
Bottom line is go with the one that is going to fit you, fit your check book, and fills your needs. You aren't going to go wrong with either one but in the event you just can't make up your mind...get both!!!!