The modified sliding midpoint rule chooses to split along the longest side of the node. It first places the splitting position at the middle. It then counts the number of points on both sides of the splitting plane and slides the plane into contact with the larger point-set. This tends to give larger cell of empty space and thus better performance because the process is biased towards cutting the empty space away from the larger point set. This also guarantees that at least one point lies on each splitting plane.
See the sliding midpoint rule for properties: they are the same.
Sliding midpoint splitting rule