The unsteady aerodynamics of floating wind turbines is more complex than that of fixed-bottom turbines, and the uncertainty of low-fidelity predictions is higher for floating turbines. Navier–Stokes computational fluid dynamics (CFD) can improve the understanding of rotor and wake aerodynamics of floating turbines, and help improving lower-fidelity models. Here, the flow field of the NREL 5 MW rotor with fixed tower, and subjected to prescribed harmonic pitching past the tower base are investigated using blade-resolved CFD compressible flow COSA simulations and incompressible flow FLUENT simulations. CFD results are also compared to predictions of the FAST wind turbine code, which uses blade element momentum theory (BEMT). The selected rotor pitching parameters correspond to an extreme regime unlikely to occur without faults of the turbine safety system, and thus relevant to extreme aerodynamic load analysis. The rotor power and loads in fixed-tower mode predicted by both CFD codes and BEMT are in very good agreement. For the floating turbine, all predicted periodic profiles of rotor power and thrust are qualitatively similar, but the power peaks of both CFD predictions are significantly higher than those of BEMT. Moreover, cross-comparisons of the COSA and FLUENT predictions of blade static pressure also highlight significant compressible flow effects on rotor power and loads. The CFD analyses of the downstream rotor flow also reveal wake features unique to pitching turbines, primarily the space- and time-dependence of the wake generation strength, highlighted by intermittency of the tip vortex shedding.