Will this be a "formal" competition gun? Or is it just for friends and family outings to the clays range?
The pump action would be considered by many to be a handicap in the competition world. If you are fast enough with it; that would be your call.
The double barrels of the Stoeger would be an advantage in either formal of informal SCs. The extra shot(s) of the BPS could only be useful in the informal shooting (if ya'll choose to for go the rules).
If it was me (which it ain't), just on the merits of the guns, the O/U has two positives (speed and choke selections). While the BPS has one negative.
With that being said, I wouldn't feel at any disadvantage with my beat up old 870. I have enough shots through it (5k+) that I'm pretty quick on the pump. (Faster than some of my friends with semi-autos.)
Wyman