The plot could revolve around a power struggle between them. They both have their own strengths and areas of control in Rapture. Maybe Big Brother decides he wants more power and tries to take over Big Sister's territory. This leads to a series of battles and strategic moves as they each try to outwit the other.
A plot could be based on a mystery. There are strange disappearances in Rapture, and Big Brother and Big Sister both suspect each other at first. As they start to investigate together, they realize there's a third, more sinister force at work. They then have to work together to uncover the truth and stop this new threat. Along the way, they might start to understand each other better and form a bond that was previously non - existent.