Computationally efficient frequency-domain models can play a very important role in facilitating conceptual design optimization of floating wind turbines (FWTs). However, achieving sufficient accuracy in such models is challenging due to the nonlinear variation of the aerodynamic loads, particularly the interaction between the floating platform motions and the controller. Building on previously proposed approaches from the literature, this work implements and improves upon three methods to evaluate the influence of rotor dynamics on FWTs dynamics in frequency domain. The investigated methods rely on: coupled fixed-nacelle simulations in turbulent wind; decay tests in steady wind; and linearized analytical expressions of the steady state aerodynamic loads. The main objective is to assess the suitability of these methods for future optimization of the floating platform and the mooring system. The various techniques are compared through a case study of three semi-submersible FWTs with increasing rotor size. While all approaches have good accuracy below-rated wind speed, only the decay test approach provide good estimates of the wind-induced global responses across all tested conditions.