If I had to pick one, or buy another, and I probably will. I would buy the Mossberg.
I prefer the Mossberg's top mounted safety, not a deal breaker just a preference. I like that the Mossberg comes with a forearm strap (must have on these). The Mossberg uses an aluminum receiver, but Mossberg wisely chose to use the 590A1 barrel that is thicker/heavier so this puts the weight out front where it is needed. I like the lesser weight in the back and more weight out front, works for me. I find the Mossberg build quality over all better than the Express based Remington. The Mossberg has the ability to use the OP-Sol clip for mini-shells, with the Mossberg's feed trough the stumpy shells just pop right in, very fast. The only mods I have done to the Mossberg is replacing the plastic safety and thin mag follower with aluminum ones from NDZ.
The Remington is based on their Express line and the exterior finish and machining was less than to be desired, but functional. There were a couple of small machine marks inside the barrel in the throat area. The action was smooth and reliable and will smooth out even more with use. The Remington is all steel and the weight can benefit those who can handle full power ammo, or want/need less recoil with low recoil type 2.75"shells, although it can take 3" shells(ouch). The Remington cannot use mini=shells (1.75"). I have "a few" Remington 870s from the 1950s onward and none of them will run 1.75" shells or the 2.25" ones Cabela's sold. The Remington does not come with a forearm strap, I think Big Green needs to correct this. I found a kit on Ebay and it installed easily and has held up so far.
https://www.ndzperformance.com/