The unsteady aerodynamics of floating offshore wind turbine (FOWT) rotors is more complex than that of fixed–bottom turbine rotors, and the uncertainty of low-fidelity aerodynamic predictions, such as those of the blade element momentum theory (BEMT) codes, is higher for the former rotors. Navier-Stokes CFD can improve the understanding of FOWT rotor and wake aerodynamics, and help improve lower-fidelity models. To highlight this potential, blade–resolved analyses of the in-house compressible CFD COSA code and the commercial incompressible CFD code FLUENT were used to investigate the unsteady flow of the NREL 5 MW rotor subjected to prescribed harmonic pitching past the tower base. CFD results were compared to the predictions of the FAST wind turbine code, using BEMT for rotor aerodynamics. Improved tuning of the COSA numerical set-up enabled close matching of the FAST rotor power and loads in fixed–tower mode, and high resolution of the near field wake dynamics; similar agreement levels were obtained with the FLUENT simulations. A novel user-defined function approach, enforcing an additional rigid body motion of the rotor grid conformal to the tower motion, enabled the FLUENT FOWT rotor simulations of this study, and provided new general-purpose FLUENT functionalities for FOWT analyses. All predicted periodic patterns of rotor power and thrust were found to be qualitatively similar, but the power peaks of both CFD predictions were significantly higher than those of FAST. Inspection of the CFD profiles of blade static pressure highlighted and quantified significant compressible flow effects on FOWT rotor power and loads. The blade–resolved analyses of the rotor downstream flow field revealed wake features unique to pitching turbine rotors, primarily the space- and time–dependence of the wake generation, highlighted by the intermittency of the tip vortex shedding.