According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = m*a).
If you apply the same amount of force to both boxes, the box with fewer books has less mass. Therefore, it will experience a greater acceleration compared to the box full of books, which has more mass.
Thus, the correct statement is:
The box with fewer books will accelerate at a faster rate.