[Galadriel55]

There is also this point which was mentioned before but not really elaborated on: the Mordor forces were firing heads over the walls of the first couple levels, and some small loads that would explode into fire. Gondorians were most likely firing large blocks such as you see in the movie. A catapult shoots lighter loads much farther than heavier loads. Gondor did not, for a fact, have anything that would equal to Mordor's explosive loads, and what's the point of firing heads at the orcs?

As for the preparation Denethor would have done, remember that Minas Tirith is unassailable. You can't break the walls with catapults. The Gondorians laughed at Sauron's catapults, because they would not do much harm to the walls. Denethor does not need to prepare a defence for a catapult attack, he has one already.

ETA: and yes, as Mumriken said, height could give advantage to, for example, archers, who shoot on a much flatter parabola. But not so much catapults.