Tough Call
I'll give you the short answer: As much as I love my 870 (although it's a righty that I shoot left handed) I would choose the BPS hands down.
To expand (and I haven't read any of the other posts)
I can say this with authority because I went through the same dilemma when I was purchasing my wife a shotgun. I don't remember what predicated looking into the BPS, but it was something about bottom ejection and ease of use for LH and RH shooters.
I really like that the spent hulls go straight down at your feet. I do think that the flexibility of the 870 as far as loading, accessories has something going for it.
I will agree that the BPS is indeed more finished than the 870 express. My wife's is in 20 ga and has cut checking (as opposed to the stamped 870) that was really pokey when we first got it). Being a field gun I prefer matte barrels, but it came with a shiny blue, which I can live with. I actually prefer the Parkerized finish of the 870, but that's just me. IRRC the barrel is overbored on the BPS for better patterns.
I know how to take down my 870 blindfolded and I don't think that it's too difficult, nor have I had any problems mechanically with it (except when I forgot to clean the firing pin channel and was getting light strikes). It's my go-to duck gun and has seen plenty of abuse (as well as a couple of stock refinishes. On the other hand, I have never completely disassembled my wife's BPS, usually because it gets so little use and spends most of her time on a rack in her closet as her HD gun. From the outside looking in it seems that the 870 is easier to fully dissassemble.
As much as I love the 870 and the sentimental value it holds if I was in the market for another pump shotgun the BPS would be the front runner. For grins you might look at Ithaca Shotguns, from what I remember the Browning design is nearly identical to those guns.