Trebuchet tended to be more imposant than mangonel, but it's not the main difference. Main difference was probably the projectile trajectory. It was the result of a difference of conception between trebuchet and mangonel. For counterpoise system, Stoffel explained it with more simplicity and efficienty that I did. Point this counterpoise system difference directly affected the balistic of the engine. In "rest" position the trebuchet beam was vertical, when he was slightly inclined toward the target for the trebuchet. System to release the sling was also different for the treb and the mangonel, always because the projectile wasn't intended to have the same course. Methode to calcul the shot was also different, mangonel played on the lenght of the sling rope as well as the impulsion exerced by crew on the counterpoise when the beam was released ect ...
Trebuchet was possibly a dangerous engine (for crews) but mangonel was more it seems. Mangonel requiered also more skilled crew (training in team for traction on the counterweight to increase swinging movement) and more skilled engineers. Probably the mangonel was more accurate than the trebuchet, but requiered more training and skilled crews. It's perhaps expectation but the trebuchet had perhaps better range.
To finish with projectile trajectory difference it implied that trebuchet were used both to attack and defend strongholds, when mostly mangonels were used to attack, Because of the relativly low course of the projectile for the last. Trebuchets with a more like "bell" course could be used behind walls to harass besiegers.
Compared effictness of both engine is not really the question. Did the design made a difference : certainly yes. It's a bit like to said a flail is a mace with a slightly different design, use and effect are the same as well as skill and training to master the weapon.