We investigate which control technique is the most suitable for the dynamic positioning of an overactuated platform. To this end, we develop a backstepping and a model predictive controller (MPC). The presence of redundant control inputs makes the stabilization of the position and the orientation of the platform challenging. Settling delays in the actuator thrust and angle, thrust saturation bounds, and jet rotational velocity bounds contribute to the challenge of the problem. To reduce energy consumption, we propose a technique for restricting the parasitic thrust effect. The significant energy reduction due to parasitic thrust restriction is illustrated in tables. The performance of the controllers is demonstrated by simulations, under realistic environmental disturbances, and is compared with that of a model-based PID controller previously developed, while the platform accomplishes two typical tasks. The evaluation criteria include energy consumption, robustness, and accuracy of the dynamic positioning. Results show the superiority of the MPC.