This paper analyses the numerical outcome of applying three different well-known mooring design approaches to a floating wave energy converter, moored by means of four catenary lines. The approaches include: a linearized frequency domain based on a quasistatic model of the mooring lines, a time domain approach coupled with an analytic catenary model of the mooring system, and a fully coupled non-linear time domain approach, considering lines’ drag and inertia forces. Simulations have been carried out based on a set of realistic combinations of lines pretension and linear mass, subject to extreme environmental conditions. Obtained results provide realistic cost and performance indicators, presenting a comparison in terms of total mooring mass and required footprint, as well as the design line tension and structure offset. It has been found that lines’ viscous forces influence significantly the performance of the structure with high pretensions, i.e., >1.2, while there is acceptable agreement between the modelling approaches with lower pretensions. Line tensions are significantly influenced by drag and inertia forces because of the occurrence of snap loads due to the heaving of the floater. However, the frequency domain approach provides an insight towards the optimal design of the mooring system for preliminary designs.