I have both, and like them both just fine. The controls are better placed on the Mossberg, IMO (safety on top of the receiver, slide release easier to reach without moving your hand); but if you think you might want to get a stock with a pistol grip at some point, the trigger-guard safety on the 870 works better with that.... Not that there's much reason to get a stock with a pistol grip, and there are all sorts of reasons not to use a pistol-grip-only stock... The slide on the Mossberg has a bit more play in it and feels wobbly compared to that on the 870, but it doesn't affect function, so that's a minor quibble.
It can be nice to have more than one barrel -- one for HD and others for hunting, for instance, and Mossberg barrels are much cheaper (be aware that you can get combo packages that include two such barrels, which is the least expensive way to do this if you don't mind spending a bit more money up front).
In terms of overall quality and reliability, there's not much to choose between them. Pretty much a Ford-or-Chevy thing... handle them both, or better yet shoot them both, and get the one you like.
(And if you a search, you'll find, oh, about a zillion threads on this topic... )