Like Warlord said, it depends on what you plan to do with it. A great shotgun for goose hunting is not the same animal as is one for deer hunting or home defense. The last two examples can tend to overlap though. Defense use means it needs to be compact enough to be manageable indoors. A good goose gun will not fit that requirement. Some folks, though, get all worked up in a frenzy about needing things like Vang-Comp work or the ability to change ammo types in mid firefight. IMHO, the only user that should be considering ammo choice in mid fight might be an LEO. When your home is being invaded, your only consideration should be ending the conflict, with consideration to others in the house not getting plastered in the overspray or overpenetration. Therefore, for defense, the shotgun should be a short barrel type, and ammo choice should have been made in advance based on the situation in the house. In my house, there is no danger of hitting anyone other than the target since the only other occupant will be behind me. A very bright light for target identification is a must as well. Some people here will tell you you are crazy for using a weapon mounted light since that gives away your location. I think if you're in your own house and are familiar with what is where, you'll know an unusual shape in the dark, so a very quick flash to verify the validity of the target just before squeezing the trigger will give away less advantage than the risk. If you kill a friendly, you're in deep doo doo and we all look bad.
But I digress - the Mossburg and the 870 are both very fine scatterguns. The Mossy may be a little cheaper, the Rem has a bigger variety of accessories available. Keep the barrel length to 20" or less, put a Surefire light on it, train with it, and either will be fine. Choose the one you like best after handling them, but make sure you get a configuration that suits your needs.