World Punkin Chunkin Championships 2019 is on Thursday, October 31, 2019: What is the most powerful kind of catapult?
Thursday, October 31, 2019 is World Punkin Chunkin Championships 2019. World Championship Punkin Chunkin The World Championship Punkin
You are asking two different questions. A ballista comes in last in the categories of "power" and distance. A trebuchet (full sized) is capable of handling much heavier missiles, and most likely had the most energy available, but a mangonel can throw father, though the payload is much lighter.
For a light missile comparison see the records at the 'World Championship of Punkin Chunkin". The Torsion record is over 3000 feet while the Trebuchet record is a bit over 2000, both using 10 pound pumpkins. On the other hand, T-Wrecks (a modern style trebuchet) threw upright pianos several hundred feet, and mangonels would barely get those off the ground.
If you're just looking for a "most powerful" answer the treb's the winner, but if you want a suggestion for what to build to throw baseballs or something a mangonel would be the best performer. Forget the slingshots except in really small sizes.