Response Surface Model (RSM)-based optimization is widely used in engineering design. The major strength of RSM-based optimization is its short computational time. The expensive real simulation models are replaced with fast surrogate models. However, this method may have some difficulties to reach the full potential due to the errors between RSM and the real simulations. RSM's accuracy is limited by the insufficient number of Design of Experiments (DOE) points and the inherent randomness of DOE. With recent developments in advanced optimization algorithms and High Performance Computing (HPC) capability, Direct Multidisciplinary Design Optimization (DMDO) receives more attention as a promising future optimization strategy. Advanced optimization algorithm reduces the number of function evaluations, and HPC cut down the computational turnaround time of function evaluations through fully utilizing parallel computation. In this paper, we test the performance of RSM-based optimization and DMDO using multiple benchmark problems of both analytical mathematical examples and a vehicle design. The benchmark problems cover three different scenario of using RSM-based optimization: (1) only real objective function is replaced with RSM; (2) only real constraint functions are replaced with RSM, and (3) both objective and constraint functions are replaced with RSM. The results are compared to DMDO to give recommendations of optimization method choices for different types of design problems with three criterions in performance, feasibility, and efficiency. This work provides systematic benchmark studies to help answer the following research questions: when the RSM-based method or DMDO should be chosen, and how to evaluate the performance of optimization algorithm.