This paper describes a driving simulation experiment, executed on the Daimler Driving Simulator (DDS), in which a filter-based and an optimization-based motion cueing algorithm (MCA) were compared using a newly developed motion cueing quality rating method. The goal of the comparison was to investigate whether optimization-based MCAs have, compared to filter-based approaches, the potential to improve the quality of motion simulations. The paper describes the two algorithms, discusses their strengths and weaknesses and describes the experimental methods and results. The MCAs were compared in an experiment where 18 participants rated the perceived motion mismatch, i.e., the perceived mismatch between the motion felt in the simulator and the motion one would expect from a drive in a real car. The results show that the quality of the motion cueing was rated better for the optimization-based MCA than for the filter-based MCA, indicating that there exists a potential to improve the quality of the motion simulation with optimization-based methods. Furthermore, it was shown that the rating method provides reliable and repeatable results within and between participants, which further establishes the utility of the method.