I've got both and I like both a lot. I shoot both a LOT. The Mossberg has a few advantages I like.
The controls: the action release is more convenient and more natural. More importantly, the safety. I've got an extended safety on the 870 so taking it off safe is moot. But when putting it back on safe (which should be any time you're moving, reloading, or doing anything other than shooting), it is WAY faster and easier with the Mossberg.
Size: in relation to the trigger, the receiver on the Mossberg sits about an inch father back. So a Mossberg with identical stock and barrel length will be about an inch (maybe closer to 1.5") than the Remington.
With the right amount of dry fire and live rounds, they both smooth out equally. My 870 express has the awful finish and starts rusting with almost any moisture (I'll fix that with cerakote eventually), so I prefer the aluminum receiver of the 590.