The entire axle moves as one, so, if a left wheel drops, the right wheel will move upward in response. Therefore, a solid-axle suspension is better on rough terrain because wheel-to-road contact is maintained through a wide range of vertical travel.
In an independent suspension, the differential unit is not part of the axle. Rather, it is attached to the chassis and power is delivered to each wheel by driveshafts.
Because the differential does not move with the axle, each wheel can have an independent suspension link to the vehicle. If the left wheel drops into a pothole, the right wheel doesn't move. But because the suspension piece is shorter, vertical wheel travel is correspondingly shorter, limiting the wheel's ability to maintain road contact under adverse off-road conditions.