Browning does not recommend pulling the bolt out of the BPS, and I've read that it's a royal PITA to put back in if you do pull it out. The 870s takedown is really simple.
When taking a BPS apart you only have to take out the one pin that holds the trigger group in. I repeat, only remove the one pin and leave the second in. If you do it this way the little arms (feed ramps) stay in which is the hard part to put back together. Also these little arms never need to be removed as they can be easily cleaned with a qtip when left in the gun as the bolt/other parts are not in the way. The bolt is simple to break down. Basically its 3 pieces that sit together as a unit that clamp around the slide/pump/forearm whatever you want to call it.
Weight
BPS heavier
870 lighter
Slide
BPS starts off a tad smoother but the forearm is out farther is is hard for some to use (you need long arms)
Remington not quite as smooth initially but once worn in they become very similiar, the forearm is closer to the trigger which is good for smaller stature people and even myself. I am 6' so its a personal preference and I find the pump on the BPS to be somewhat of a "reach"
Safety
BPS has the top safety used by the thumb - I prefer this style on all firearms
870 has the push button safety by the trigger.
Unloading
BPS can be unloaded w/o cycling the action
870 ammunition must be pumped through the gun. (Nothing wrong with this, just keep the muzzle pointed down and away obviously)
Slide release - both are same location
BPS feels a little more positive compared to the 870, perhaps because its a heavier spring your pushing against and a bigger piece of metal... The 870 slide release works beautifully as well.
Fit and finish
Both guns are on par with each other but I don't like how the muzzle on the BPS receives no bluing. Not sure if this is the same on the wingmaster
Reliability
The browning bottom eject works flawlessly as far as my experience goes and looks sort of neat but the 870 has a very proven track record as well. I have never had any jams with either but I bet the BPS will break down before the 870 in an endurance shooting test - both though I'm sure would handle more than most users will shoot in their lifetimes.
Loading
BPS must load from the magazine to the chamber
870 you can drop one in through the ejection port and slide the forearm/pump forward which is quicker on the reload.
They are both well made guns, whatever feels best is what is right.
I went with the BPS because it is ambidextrous and I'm LH. (I have no interest owning an 870 express). I also got the 20 gauge because it is much lighter than the 12. The 12 gauge is heavy and I would never want to carry it around. I initially felt that the bps came up to my eyes so well but my trap shooting with it hasn't shown that. I think the LOP is too long.
If I was right handed I would probably go with 870 wingmaster for a second time around but your experiences may vary.