Under-actuated robots are very interesting in terms of cost and weight since they can result in a state-controllable system with a number of actuators lower than the number of joints. In this paper, a comparison between an under-actuated planar three-degrees-of-freedom (DOF) robot and a comparable fully actuated two-degrees-of-freedom robot is presented, mainly focusing on the performances in terms of trajectories, actuator torques, and vibrations. The under-actuated system is composed of two active rotational joints followed by a passive rotational joint equipped with a torsional spring. The fully actuated robot is inertial equivalent to the under-actuated manipulator: the last link is equal to the sum of the last two links of the under-actuated system. Due to the conditions on the inertia distribution and spring placement, in a simple point-to-point movement the last passive joint starts and ends in a zero-value configuration, so the three DOF robot is equivalent, in terms of initial and final configuration, to the two DOF fully actuated robot, thus they can be compared. Results show how while the fully actuated robot is better in terms of reliable trajectory and actuator torques, the under-actuated robot wins in flexibility and in vibrations at a given configuration.