It depends on what your criteria is for choosing one or the other. Assume quality is equal (which is asking a lot for current production 870s), the controls and loading are very different. The 870 has a slide release at the front ejection side of the trigger guard and a safety at the rear of the trigger guard. The lifter is spring loaded and will come back down when you finish loading a shell. By comparison, the Mossberg 500/590 shotgun lifter stays up and the way I load it is 1 in the ejection port, close it, flip the shotgun over, drop a shell into the loading port and push it in with the next shell. This is much faster than I've ever been able to load a Remington (or Mossberg 930 that has the 870 style lifter). Mossberg's controls (unless you get a Maverick 88 which has a safety on the trigger guard) are a left side slide release at the rear of the trigger guard and the safety on the top of the receiver. If you want to put a pistol grip on it, get an 870 or a Maverick 88. I have a 500, 590, and a 930 by Mossberg and I'm wearing a Mossberg hat while I'm typing this so the side where my loyalty lies should be pretty clear but that's based on my preference. I don't think Mossberg is objectively better, but I prefer the controls, loading, full length single piece magazine tubes, and the receivers being drilled and tapped from the factory (I use micro red dots). Personally, the only reason I would buy an 870 is if I were intent on putting a collapsible pistol grip setup on it. I've owned 3 and only 1 of them was reliable.

Left to right; 500, 930, 590, Maverick 88. The Maverick 88 is my dad's.