In more closed positions the bishop’s actions are hindered by the pawns. So therefore the player who has the bishop pair should strive for opening up the position.
But there is another point to it, often missed by commentators. When you are in sole possesion of the bishop pair clearly your opponent misses one of his bishops. Therefore he might be weak on the squares that are not covered so well anymore.
I only started to think about this after a grandmaster made a remark to this extend on Playchess.com. You will find a great example in the game between Byrne and Fischer. Note the weakness of the light squares in white’s position!