This ball handling drill is going to work on developing both hands at the same time, and work on handling the basketball on the move. When a player is dribbling a basketball in transition they may not be able to slow down before they make their move past the defender. It will usually just be a quick reaction to the defender, and then a quick dribble move to get past them. If you are a primary ball handler this is a great drill to do.
Also, by doing the basketball drill with two basketballs instead of just one, you add another level of difficulty to the move. The player must be able to handle a basketball equally well with either hand. This will help to make the player more complete, and maximize time in the gym.