Stratocumulus clouds play a central role in the radiative balance of the Earth, and thorough understanding of their structure and dynamics is essential for accurate climate- and weather-prediction. Laboratory and numerical experiments have in combination with field measurements over the last few decades greatly improved our knowledge about how the stratocumulus-topped boundary layer (STBL) evolves, but important questions still remain open; e.g. regarding the role of turbulence. In this study, we use results from large-eddy simulations and observations from the POST and DYCOMS-II field campaigns to examine properties of turbulence near the cloud top. More specifically, we determine the level of anisotropy across a range of scales and investigate how this may affect cloud-top entrainment - the process in which the STBL grows upwards over time. Focusing on turbulence ~100 m below the cloud top, we see remarkable similarity between daytime and nocturnal flight data covering different inversion strengths and free-tropospheric conditions. Typical-resolution LES of the STBL (based on POST flight 13 and DYCOMS-II flight 1) captures the observed characteristics of below-cloud-top turbulence reasonably well, but the simulation results are sensitive to changes in grid spacing and the choice of subgrid-scale mixing length. Using a fixed vertical grid spacing of 5 m, we find that decreasing the horizontal grid spacing and increasing the subgrid-scale mixing length leads to increased dominance of vertical fluctuations, increased entrainment velocity and decreased liquid water path. Our analysis supports the suggestion that entrainment parametrizations (used in e.g. climate models) could potentially be improved by accounting more accurately for anisotropic deformation of turbulence in the cloud-top region.