Two of the most common modes of oscillation of single degree of freedom wave energy converters are heave and surge, which are respectively exploited by heaving point absorbers (HPAs) and oscillating surge converters (OSCs). Notwithstanding essential hydrodynamic differences, both devices are very often described by the same linear model structure. However, if the linearising assumption of small amplitudes of motion is challenged, especially under controlled conditions, different (and significant) nonlinearities are excited in the devices. This paper studies the differences between the hydrodynamic forces in HPAs and OSCs under controlled conditions, considering a nonlinear representation of Froude-Krylov forces and viscous drag effects. Results show that HPAs are predominantly affected by nonlinear Froude-Krylov forces, while the most important hydrodynamic forces in OSCs are due to diffraction and radiation effects. In addition, viscous drag appears to have little relevance in HPAs but a significant influence in OSCs.