The BPS is still quite big, and usually the heaviest thanks to its steel reciever (both the 870 & 500 use aluminum, IIRC).
In 20 guage all three are functionally equivelant. Each has some small advantage that may lend it better to an individual, or to some small niche' use, but to be honest none of them do anything the other two cant do well. This is chiefly because all three manufacturors have at least two reciever sizes.
The difference would be much more drastic if you wanted a 410 or 28. To my knowledge, Mossberg is the only one of the three that has a pump action reciever smaller than 20 gauge.
Thus the Mossberg 500E (.410 bore field) is built on a reciever that is both low weight aluminum AND gauge scaled. The 870 is aluminum, but not scaled. The BPS 410 is NEITHER aluminum nor scaled to gauge.
Thus the difference between the 500 and BPS is pretty extreem in the sub-bore catagory, but the field is essentially level in 20 gauge, as they all use the same size.
IMO:
* The BPS is heavier (not necessarily bad, depending on application) and more nicely finished
* The 870 is the best ballanced, and easiest to field strip
* The 500 is cheap and reliable ... but is a pain in the butt to clean (uncaptured disrupter arms) and the barrel swap issue is annoying.
Thus, i would only recommend the 500 when seeking a 410 bore, as that is the only time its specifications are 'better' enough to offset the issues inherant in that platform.
For the 20 gauge you are seeking, I would choose between the Browning and the Remington based on your weight preference, provided neither feel too objectionable when shouldered.