In this paper we discuss two different approaches to simulation, discrete event simulation and system dynamics. Both have been used widely in the health care domain, although there are fewer applications of system dynamics. The aim of this paper is not to give a comprehensive survey of the literature, but rather to discuss whether the choice of methodology is purely the personal preference of the modeller, or whether there are identifiable features of certain systems that make one methodology superior to the other. We illustrate the use of these techniques by considering two case studies, a simple discrete event simulation model of HIV/AIDS and a system dynamics model of the UK cardiac surgery system. We attempt to draw up some guidelines to assist the modeller in making the choice of technique