Computational fluid dynamics (CFD)-based numerical wave tanks are valuable tools for the development and evaluation of energy maximising control systems for wave energy converters (WECs). However, the exaggerated body motion amplitude, which can be induced by the energy maximising control system, challenges the commonly applied mesh morphing method in CFD, due to the resulting mesh distortion and subsequent numerical instability. A more advanced mesh motion method is the overset grid method, which can inherently handle large-amplitude body motions and has recently become freely available in the open-source CFD software OpenFOAM. The overset grid method can, therefore, potentially eliminate the mesh distortion problem, hindering the simulation of WECs under controlled conditions. To evaluate the capability of the overset grid method for control studies of WECs in an OpenFOAM numerical wave tank, this paper presents a detailed comparison of the overset grid and mesh morphing methods, considering five test cases of increasing complexity. The test cases range from a static equilibrium test to the modelling of a controlled WEC, and good agreement is demonstrated between the two mesh motion methods, except for the case of the controlled WEC, when the device motion becomes large, and the mesh morphing simulation crashes. The runtimes for overset grid simulations are observed to be approximately double the time required for the mesh morphing simulations.