Unlike in the case of open kinematic chains (OKCs), where the stability results for many control schemes are well established, for general closed kinematic chains (CKCs), rigorous stability results are rare. In this paper, we compare our recently developed control method, namely the singular perturbation formulation (SPF), to a control method based on input-output linearization (IOL) of a differential algebraic equation (DAE) model of CKCs. We show the advantages and disadvantages of each method from a theoretical as well as an implementation standpoint. The comparison indicates that our SPF approach is superior in terms of large validity domain, ease of control, implementation, and good performance of the closed-loop system