You can read these post all day and you will get nowhere fast. for every 100 that love the BPs another 100 will hate it, and vica versa.
They are both great guns, very very clean track records. Although they have a couple small differences, they are all strictly preferential and the end result is the same...BANG.
HOWEVER! they both feel completely different. The BPS is physically bigger that the 870 in most dimensions. This is definitely not a good or bad thing, but if you are a remington rifle guy, you may find the palm swell on the BPS quite large in comparison to the remington. The fore grip is also slightly larger.
The size and dimension differences are unarguable facts, the only way you are going to be able to make up your mind is to have your local shop place both of them on the counter in front of you and let you shoulder each gun.
One will "feel" right. That's the one you buy, regardless of the brand.