The vibration mitigation performance of different feedback controlled damping devices for cable vibration mitigation is investigated. A model-based designed LQG controller estimates the vibration state based on a validated linear cable model. The main nonlinearity of the connected system damping device - cable is compensated by its inverse function. The simulated damping devices are actuator and controllable damper without any actuator/damper dynamics. It is assumed that further constraints such as minimum or maximum force limitations do not exist. The theoretical study compares the potential of vibration mitigation using a feedback controlled actuator and a feedback controlled damper. The comparative study is simulated for two positions of the damping device. One is near the anchorage, which is the only possible position on a real cable-stayed bridge. The other position is characterized by the largest cable displacement within the frequency range of the first four modes. In order to guarantee a fair comparison, the optimal controller parameters are determined for the active controlled actuator and semi-active controlled damper for both positions. The simulation results demonstrate, first, that active controlled actuators can hardly mitigate vibrations more effectively than semi-active controlled dampers because vibration energy must be dissipated. Second, the position of the damping device shows a negligible influence on the mitigation performance because smaller displacements and therefore smaller velocities near the anchorage are compensated by larger actuator/damper forces.