Stellar differential rotation can be separated into two main regimes: solar-like when the equator rotates faster than the poles and antisolar when the polar regions rotate faster than the equator. We investigate the transition between these two regimes with 3D numerical simulations of rotating spherical shells. We conduct a systematic parameter study which also includes models from different research groups. We find that the direction of the differential rotation is governed by the contribution of the Coriolis force in the force balance, independently of the model setup (presence of a magnetic field, thickness of the convective layer, density stratification). Rapidly rotating cases with a small Rossby number yield solar-like differential rotation, while weakly rotating models sustain antisolar differential rotation. Close to the transition, the two kinds of differential rotation are two possible bistable states. This study provides theoretical support for the existence of antisolar differential rotation in cool stars with large Rossby numbers.