I guess I can elaborate a little if no one else is going to step in. There are two reasons I prefer the BPS. 1) it's abidexterous. The safety is on top, the ejection is out the bottom. That means that anyone can shoot it. It also means no throwing empty hulls across your hunting partners. 2) it can't be jammed. The 870 has always had a problem with people who don't "push it til it clicks" when loading shells into the magazine. when that happens that shell get stuck behind the loading gate in an abnoxious jam. The bps can't do that. Now 870 fans will jump up and down and say they've hunted with an 870 for 472 years and they've never done that. Well i've done it. It happens when you're hunting ducks in january and your fingers are frozen. It happens in september when you're loading shells as fast as you can dove hunting. I'd be scared to death it would happen in some type of self defense situation.
Both guns are impervious to mud, ice, water, etc which is important to me. Both guns are quality pieces of equipment. The BPS feels smoother but probably shoots a little slower and seems to have a longer pump stroke for equal sized chambers. The bps can be disassembled completely and easily with no tools.
My first 870 (a 20ga I no longer own) would leak gas around the bolt and I would get powder and gas in my eyes. That's why I sold that gun. Since then I've had 2 that didn't do that although I've had 1 that sometimes had troubles with resetting the hammer.
I've never had, seen, or heard of BPS malfunction. They are easy to load, strip, shoot, and carry. I honestly can't think of a reason to own a different shotgun currently in production.
My favorite gun is a Winchester and I have no allegiance to either company.