The present study focuses on the analysis of the quadratic transfer functions (QTFs) that act on a vertical and free-floating wave energy converter. The methodology employed in this study involves two primary steps. First, a thorough analysis of the QTFs related to sum- and difference-frequency wave loads is conducted using the open-source NEMOΗ code. Then, a comparative analysis of the findings is conducted with the results obtained from the commercial software ANSYS-AQWA. In NEMOH, the QTFs include quadratic terms that are the product of first-order velocity components representing nonlinear effects due to wave-wave interactions and second-order potential terms resulting from solving the second-order velocity potential. These additional nonlinear effects are not accounted for by the quadratic terms. ANSYS-AQWA employs a different approach and does not take into account the effects of second-order scattered waves; rather, it applies the Pinkster approach. A comparative analysis of the aforementioned methodologies reveals the significance of QTFs in the mooring dynamics of wave energy converters.