It does have to do with longitudinal stability like you mentioned. The Cessna, being a high wing, has constant airflow from the trailing edge of the wing down to the stabilizer creating a significant amount of tail down force. Even as flaps are added the center of lift moves aft creating a nose down tendency. This is balanced by the air rushing over the wing and striking the elevator creating a dynamic balancing force or tail down force. Because of the additional down-flow air from the high wing, not as much control surface is needed to provide pitch stability.
Piper, being a low wing, has the stabilator with the servo on the back. When the relative rushes over the upper surface of the wing and is deflected downward off the trailing edge, it goes nowhere even near the stab which reduces its effectiveness overall. The servo on the back provides a dynamic balancing force so the airplane is not over-controlled by simple stabilator movements. When flaps are added to its configuration notice the nose of a Piper will drop much more than a Cessna. As the center of lift moves aft with flaps it creates a nose down moment. In a low wing there is no force to counter-act the nose down attitude where as the high wing has the air over the main wing striking the tail providing the tail down force or dynamic balancing to the aircraft longitudinal axis.
To sum it up, the Piper, due to airflow patterns off the wing and their effect on lpitch stability, needs a larger control surface to provide enough longitudinal stability. The Cessna has a much greater force acting on the tail with the high wing deflecting the wind off the trailing edge to the elevator which increases its effectiveness and ultimately results in less need for a larger control surface.
Clear as mud right?