I own both:
1992 Remington 870 Express Magnum w/ 18" cylinder bore police barrel, wood stocks.
2007 Mossberg 500 w/ 18.5" special contract overrun Accu-choked heavy-walled police barrel, wood stocks.
Here's my opinions on the both of them.
The most versatile is of course the Mossberg. It has an 18.5" barrel which makes the entire gun very short and I can change chokes in it for whatever kind of pattern I desire, from buckshot to birdshot to slugs. I keep Improved Cylinder in it for home defense. It is the only shotgun I have that can serve every purpose, from home defense to hunting. The gun balances well, mostly due to the short barrel. Long-barreled Mossbergs tend to be muzzle-heavy because the receivers are lightweight but with short barrels this is eliminated for the most part. The action is pretty smooth, not as smooth as my 870 but not bad at all. The safety is mounted on top of the receiver which is excellent when using regular stocks, but the worst possible location if using any pistol-grip configuration.
The 870 has only an 18" cylinder bore which cannot be changed, so it is strictly for close-up work like animals in the yard and home defense. The action is much smoother than my 500, but the 870 is also 15 years old. It balances well with short or long barrels due to the all-steel receiver making the back end of the gun have some heft to it to counter the weight of 28" barrels. The safety is mounted on the trigger guard which makes it very nice if you plan on using any type of pistol-grip configuration.
I use nothing but standard stocks on my shotguns so I do think the Mossberg has the edge there slightly due to the location...however, the 870's safety isn't anything to be worried about. I can flick the safety off the same speed on both shotguns, but when switching the safety back on the Mossberg has a slight advantage since you don't have to change your grip on the gun.
If I had to pick one over the other, it would be very hard. I love them both. I say go with whichever one feels best in your hands because as far as functionality and toughness, both are equal.