Sudden stratospheric warmings (SSWs) can have major impact on surface wintertime weather, especially at mid‐high latitudes. We do not yet have a complete understanding of why some of these events influence our weather more than others, but one factor may be the dynamical nature of the SSW; whether it involves a split or a displacement of the polar vortex, and one way to explore this is through comprehensive climate models. Here, we analyze the stratospheric dynamics of SSWs within models from the sixth Coupled Model Intercomparison Project (CMIP6). All CMIP6 models simulate SSWs to some degree, although we find a persistent bias in the relative underrepresentation of split vortex events. When comparing with CMIP5 models, large biases persist despite significant model improvements in resolution and in representing atmospheric processes. We show that the simulated displacement frequency is strongly related to climatological lower stratospheric eddy heat flux. The split frequency, on the other hand, is not related to lower stratospheric eddy heat flux, but is strongly related to both the vortex geometry (aspect ratio) and lower stratospheric zonal winds. This suggests that those models with a large positive bias in zonal winds may inhibit the propagation of zonal wavenumber 2 planetary waves from the troposphere, which are associated with split events. Our results suggest how future model development may address these longstanding biases.