The growing prospect for large farms of floating offshore wind turbines requires a better understanding of wake effects for floating turbines. In this work, large eddy simulations with an actuator line model are used to study the wake of the NREL 5 MW reference turbine mounted on the OC3-UMaine spar and OC4-DeepCwind semi-submersible platforms. The simulations are carried out in the Simulator fOr Wind Farm Applications (SOWFA) coupled with OpenFAST for the platform and turbine motion. The wake location, deficit, and turbulence levels are compared for the two floating platforms and equivalent fixed-turbine cases. The effects of neutral versus stable atmospheric conditions are also compared. Most notably, floating-turbine wakes are deflected upwards compared to fixed-turbine wakes, because of mean platform pitch. The spar wake deflects upwards more than the semi-submersible, while the stable atmosphere increases this vertical deflection compared to the neutral. The time-varying rotor motions do not significantly affect the mid-to-far wake, though the stable atmosphere shows larger fixed-floating differences in horizontal wake fluctuations.