Given the choices I would go with the 870 since you wanted to add capacity. It would be a pain to upgrade the mossberg. I personally went with the 590a1. Easy to add a mag extension like the 870, but has a tapped receiver if you ever want to add an optic. Biggest selling point for me was the location of the controls since I shoot long guns lefty.
I purchased a Remington 870 this past summer, but I've not had a chance to shoot it yet. It was purchased primarily as a home defense weapon. Mine is not the synthetic, but it is a tactical. When we bought it, we also purchased an collapsible stock with pistol grip so that it would work for either myself or the wife.
The only issue I've seen so far, considering I've not fired it yet, is that to properly disassemble it for cleaning, I have to remove the stock/pistol grip to get it apart. I'll need to hunt up the box the stock/pistol grip came in to see what brand/model it was.
So, if you go with a pistol grip, keep that in mind. I don't know if there are other collapsible stocks/pistol grips that will fit the 870 without having that issue, but you might look into it.
There isn't one that is better than the other. I like remingtons better overall but there are some things I like better about the mossberg. I like that the ejector can easily be replaced. I like that the shell latches/interupters aren't staked in. The safety is in a neat location I think. You really need to own both. So just buy the one that pops up first for a good deal.
I've never understood wanting a pistol grip on a shotgun, but to each their own. Mossberg makes good shotguns, I have the 930 SPX and it kind of rocks. The 590A1 as a thicker barrel wall than the 500.
Mossy all the way for me. 10,000+ rounds, and never had a hiccup. My best friend ran 6,000ish rounds through his mossberg without cleaning it, and never had a hiccup. His gun was covered in rust and mud since it lived in his pipeline rig in North Dakota
870 hands down. Tried both, prefer the safety by the trigger. Don't have to reset my thumb for proper grip. BTW, don't spend extra for bling. In the dark the bad guy can't appreciate it, and when the lights come on they ain't seein' nuthin'!
What happens when you grab any other long gun or a handgun for that matter ...there only handful crossbolt safety firearms out there, and most of them are a source of complaints (ie Marlin and Benelli).