This is my favoiret department when someone ask a question like this.
Remington 870s are a good gun. The only major problem is with their matte finish and blued finish. These will get rust on them so you need to be carefull with finger prints. Allthough any gun will get rust without proper care.
The Mossberg 500 is also a good gun. These are a very tough shotgun. Your 500's have plastic parts but I rarely hear people complain about them.
As for them both carrying total ammount of ammo it really does not make a difference. Mossbergs go from 6 to 9 shell compacity and I think remington is the same on that if im not mistaking.
One other thing that will be good to do is to try and shoot each one and see how it feels to you.
Other than that just flip a coin.