Designing, optimizing and controlling a wave energy converter requires the construction of a mathematical model in order to simulate the behaviour of the device. Given the nonlinear nature of fluid-structure interactions, the definition of the model is not straightforward and should take into account the specific application it is intended for. Two of the most important characteristics of a model are the computational time and the expected accuracy, which usually are mutually conflicting. The inclusion of nonlinearities potentially increases the model accuracy, but at a higher computational price. Considering a heaving wave energy converter with and without the application of latching control, this paper studies and compares nine different modelling options, eight of which are based on potential theory and consider nonlinear Froude-Krylov and viscous drag forces, while one is based on fully-nonlinear computational fluid dynamics. The value of including nonlinearities in the hydrodynamic model is discussed in relation to the computational cost of the eventual accuracy benefits, under a range of scenarios.