Flexible multibody simulation, subject to holonomic constraints, results in nonlinear differential algebraic systems. As computation time is a major issue, we are interested in applying model order reduction techniques to such multibody systems. One possible method called Proper Orthogonal Decomposition is based on minimizing the displacements’ Euclidian distance while the more recently presented method Smooth Orthogonal Decomposition considers not only displacements but also their time derivatives. After a short introduction to the theory, this contribution presents a comparison of both methods on an index-reduced system. The methods are tested against each other in order to identify advantages and disadvantages.