There are two popular parallel programming paradigms available to high performance computing users such as engineering and physics professionals: message passing and distributed shared memory. It is interesting to have a comparative evaluation of these paradigms to choose the most adequate one. In this work, we present a performance comparison of these two programming paradigms using a computational physics problem as a case study. The self-gravitating ring model (Hamiltonian mean field model) for N particles is extensively studied in the literature as a simplified model for long range interacting systems in Physics. We parallelized and evaluated the performance of a simulation that uses the symplectic integrator to model an N particle system. From the obtained results it is possible to observe that message passing implementation of the symplectic integrator presents better results than distributed shared memory implementation.