We consider the problem of velocity estimation for a control moment gyroscope inverted pendulum. To this end, we a consider model-free differentiator, a model-based linear observer and a model-based nonlinear differentiator. The proposed designs are implemented in hardware and the closed-loop system performance in the stabilization task is compared. Moreover, we show that the considered system cannot be partially linearized via a change of coordinates, and thus is not suitable for a recently reported class of nonlinear observers.