I like them both, but my preference is the 500 given the choice between the two.
Also take a look at the 590. They are well built. They are a good bit heavier but you'd only notice if you were carrying it for hunting.
The guys that prefer 870s always say that the 500s are rattle traps. The guys that prefer 500s know how to carry them so that they are quiet.
For the most part the 'cheap' impression of the Mossberg is from the loosely fitting charging bars that rattle if you don't keep your hand on them. That loose tolerance is your friend when it comes to reliability in harsh freezing hunting conditions.
I can say that in my entire life of being surrounded by Mossbergs, I have never had to repair one because they simply don't break.
To me , another advantage is the location and size of the slide release. With simple muscle memory, it is nice and easy to push in with heavy gloves while the 870 is a small button that is difficult to get to in a hurry.
You can up the capacity of an 870 by adding a tube extension while with the Mossberg, you are stuck with the capacity that you bought.