The input and ouput simulation data of the THOR GCM for Dynamical and radiative effects resulting from the deep non-hydrostatic vs deep quasi-hydrostatic equations in the global circulation model THOR with an added non-grey radiative transfer scheme Global circulation models (GCMs) play an important role in contemporary investigations of exoplanet atmospheres. Different GCMs evolve various sets of dynamical equations which can result in obtaining different atmospheric properties between models. In this study, we investigate the effect of different dynamical equation sets on the atmospheres of hot Jupiter exoplanets. We compare GCM simulations using the quasi-primitive dynamical equations (QHD) and the deep Navier-Stokes equations (NHD) in the GCM THOR. We utilise a two-stream non-grey "picket-fence" scheme to increase the realism of the radiative transfer scheme. We perform GCM simulations covering a wide parameter range grid of system parameters in the population of exoplanets. Our results show significant differences between simulations with the NHD and QHD equation sets at lower gravity, higher rotation rates or at higher irradiation temperatures. The parameter exploration shows the relevance of choosing dynamical equation sets dependent on system and planetary properties.Climate states of hot Jupiters seemed to be more diverse than previously thought. There are exceptions to prograde superrotation. Overall, our study shows the evolution of different climate states which arise just due to different selection of Navier-Stokes equations and approximations. We show the shortcomings of approximations in GCMs made for Earth, but used for non Earth-like planets.