I own both, and there are occasions where I'll prefer one over the other. I think it's probably important to note that I'm comparing a very well-maintained 1970s-vintage 870 Wingmaster to a 1990s BPS. My newer 870 Express is a bit clunkier-feeling than my Wingmaster.
In a goose blind, I'll take the BPS every time. Bottom eject is a bonus, the BPS comes straight up and onto my shoulder.
For pheasants - when I'm not carrying my favorite O/U - the Wingmaster fits the bill. I'm not as comfortable with the safety as I am the tang safety on the BPS (and my O/U), but it feels better coming up and swinging into a bird than the heavier-feeling BPS.
Overall, for most purposes outside the goose pit, I'd probably give an edge to the Wingmaster over the BPS. Both are excellent shotguns. If you're a lefty, I'd probably pick the BPS.