I'm not sure what type of quail you want to hunt, but my experiences with these types of guns (heavy 12 Gauge pumps) on quail have been 100% negative. The fast, surprise flushes and short shot windows on Western quail mean that the birds are often up, away and gone before you overcome the inertia of a big, heavy gun and even get a chance to mount it.
People do use them on passing doves, though they're not ideally matched to doves. The guys who use them seem to be waterfowlers who want some pre-season practice on passing birds, and I think they get what they want out of it, along with some fun and some doves to eat.
The 887 has features that understandably appeal to a serious waterfowler. However, I think it handles terribly, with really odd balance. It's no 870, that's for sure. I really prefer the Benelli plastic-shelled pumps' handling characteristics. Early 887s were really crappy, but reports here seem to indicate that Remington took care of at least the blatant problems with parts not fitting together.
The 870 in 3.5" handles pretty much like any 870, which is to say, very well for an inexpensive pump gun. If I were going to shoot doves with any of these, it would be the 870, I think.
The Mossberg has an oversized bore and heavier weight, which make it ideal for 3" to 3.5" waterfowl loads. It's really designed for the near-10 Gauge 3.5" loads, so that you can use the same gun for ducks and geese with good results. The heavy weight cuts down on felt recoil and smooths out the swing for passing shots. However, it's about the last gun I'd want to use for quail.
Definitely get your hands on these guns before deciding. They are different.
My personal recommendation would be to get a gun for upland and one for waterfowl, and choose one or the other for pheasant hunting, depending on the exact conditions. If you want to keep up your pumping skills for waterfowling (mine suck because I seldom use pumps), you can get, say, a 20 Gauge 870 and use it for upland birds, and get a duck/goose gun that's really ideal for the purpose.
Looking for a single good gun for quail to geese is almost like trying to find a rifle for prairie dogs to moose.