We have one BPS here, in 12 ga.
And about a dozen 870s in varying formats in 12 and 20 ga.
Both are good solid shotgun designs, have great 'heft' and 'feel' and will do a workmanlike job at what pumpguns do.
But you can't fieldstrip a BPS. You can't swap out a bolt assembly if the firing pin breaks in the bolt that's in the gun, or if the extractor goes down or freezes up in a duck blind. You can't just swap out a trigger plate assembly if a small part in the fire control mechanism fails (though admittedly, both of these are low probability events in either of the guns). Spare barrels are everywhere for 870s- not so for Brownings. There are bunches of stocks, forearms and all manner of accessories necessary and useless for the 870- the market does not support the Browning in such a fashion. Remington's flexible tab lifter makes serious misfeeds unlikely, but if you manage to make a BPS hiccup by shortstroking it the gun is likely down till you can get the barrel off and clear it.
If you're the sort who never has to wash mud off legs and boots before your wife will let you inside her house (or worse, strip down outside first like a miscreant 5-year-old), you can get by with the Browning. If you never spend hours here and there working heavy cover behind a bird dog and the in-between times wading through waist-high broomsedge, filling all your pockets and every other recess on your person with leaves, twigs and enough seed fluff for a bird condominium, then the Browning will do you fine. If you never have to use your shotgun to paddle/pole your duckboat, get the Browning. If you are immune from gravity and never fall down into water/mud/sand or any combination thereof, or never let your gun escape from cold/wet/slippery/numbed fingers into such things, get the Browning.
But if you want a gun you can use HARD for whatever necessities come along, then drag home, hose off, strip down, clean up, relubricate and have it come out looking for more of the same, then you need an 870.
It's been that way for more than 50 years now, and it hasn't changed. I hope it never does.
Regards,
lpl/nc