That is the Ford-Chevy debate of the shotgunning world, you realise this. I'm going to assume you are talking pump actions...

The Mossberg is a little less expensive, but the M500 (single action bar) is cheeper than the Remington 870. Both the Moss M500 and M590 (dual bars, 95% of them are in tactical configuration, and they can't use the M500 sporter barrels) use a tang mounted safety. That makes them a little better suited for southpaws. Becuase of how they do thier endcaps, you can't mount a magazine tube extension.

Remington 870 is just as common, but a little more expensive. It has a push button safety forward of the trigger gaurd, which is well suited to right handed use. There is a left handed version available, but it is made in limited numbers, and as a lefty, you can learn to hit it with the supporting hand while doing a press check on the tube and lifter. You can put magazine tube extentions on the 870 easily, some production runs might need the use of a small drill, but nothing that needs a gunsmith.

Let's toss in the Mavrick 88 for grins and giggles. Mavrick is a line owned by Mossberg, and their 88 is basically a Moss M500 wioth a push button safety. It can use a lot, but not all of the same parts as the Mossberg.

Both the Mossberg and the Remington are super, super common. Between the two of them, they probably hold half the market on pump guns. That means that you can get accessories and mods for both pretty much anyplace. Cabela's, Gander Mountain, Sportsman Guide, etc, all have replacement barrels. Everyone who makes tactical gizmos supports both of them. Having shot the Moss 500 and 590, the Mav 88 , and the Rem 870, I'd say they are of equal quality, really. The Mossberk 500 and 950 and the Remington 870 are still serving in active duty in Afganistan and Iraq, despite the adoption of the Benelli M4 and that clumsy little attempt at an underbarrel (don't know it's model number, sorry).

What I would say is, try them in the shop, see what you like best. But get a 3" chamber- you probably won't NEED it, but you will have it if you ever do. I also find that the longer chamers seem to feed a little cleaner with hulls that have been reloaded too many times.

My personal choice is the old Ithica M37. I wouldn't run 3" shells in it, even if the chamber could handle it, in an origonal, but the new production 37, and the 80s era 87 can do it. It is hard to argue with a reciever milled from a single, monolithic block of steel, and possibly the lowest part count of any repeating shotgun. (I'm not sure if the new production 37s use the milled reciever; I know the 87s used an investment cast one.)