
I have divided catapults into these categories: Finger-launch, spring-launch, rubber band, press button, chain pull, and counterbalance. Please add to, rename, and/or consolidate any categories as this discussion evolves because a fun discussion always trumps the need for scientific data analysis (here, anyway).
I tested a wide variety of offical catapults on the 8822 Gargoyle Bridge, with the giant axes as the target. Using both logical and abitrary qualifiers such as control, launch speed, arc, distance, and aesthetics, these are my personal nominees:
Finger-launch: 1480 King's Catapult (http://www.classic-castle.com/sets/oop1991.html). Great arc and distance for a small catapult. I like using 2 x 2 round bricks than the supplied 1 x 1 rounds.
Spring-launch: 7017 Viking Catapult. The giant crossbow looks much cooler than the launcher on the Viking Ship (which is stronger). I did not try the Heavy Artillery Wagon in my test.
Rubber band: 8873 Fireball Catapult. Great control. I instantly disqualified the KKII horse saddle catapults on the grounds of ridiculousness.
Press button: None. I'm not a fan of the one mounted on the 7019 Viking Fortress.
Chain pull: None. I do not like the one that "defends" the 8781 Castle of Morcia.
Counterbalance: None. The one with 6059 Knight's Stronghold is way too weak.
Pax,
Pacificus