Floating offshore wind platforms may be subjected to severe sea states, which include both steep and long waves. The hydrodynamic models used in the offshore industry are typically based on potential-flow theory, and/or Morison's equation. These methods are computationally efficient, and can be applied in global dynamic analysis considering wind loads and mooring system dynamics. However, they may not capture important nonlinearities in extreme situations. The present work compares a fully nonlinear wave tank (NWT), based on the viscous Navier-Stokes equations, and a second-order potential-flow model for such situations. A validation of the NWT is first completed for a moored vertical floating cylinder. The OC5-semisubmersible floating platform is then modelled numerically both in this nonlinear NWT and using a second-order potential-flow based solver. To validate both models, they are subjected to non-steep waves and the response in heave and pitch is compared to experimental data. More extreme conditions are examined with both models. Their comparison shows that if the structure is excited at its heave natural frequency, the dependence of the response in heave on the wave height and the viscous effects cannot be captured by the adjusted potential-flow based model. However, closer to the inertia-dominated region, the two models yield similar responses in pitch and heave.