Future quantum communication infrastructures will rely on both terrestrial and space-based links integrating high-performance optical systems engineered for this purpose. In space-based downlinks in particular, the loss budget and the variations in the signal propagation due to atmospheric turbulence effects impose a careful optimization of the coupling of light in single-mode fibers required for interfacing with the receiving stations and the ground networks. In this work, through a variety of simulations we model the effects of turbulence on the transmission of the signal, its partial correction via an adaptive optics (AO) system and finally we compute the corresponding secret key rate for both continuous-variable (CV) and discrete variable (DV) quantum key distribution protocols. Our analysis allows us to estimate the key rate for a range of critical parameters, such as turbulence strength, satellite altitude and ground telescope diameter. The results we derive illustrate the interest of adopting advanced AO techniques in several practical configurations.