Accurate trajectory planning is crucial for safe driving of autonomous vehicles in critical driving manoeuvres. However, using simple models for trajectory planning in such conditions may result in unrealistic or unsafe trajectories. This paper evaluates various combinations of models, i.e., over-actuation and vehicle and tyre models, for trajectory planning in critical conditions. The trajectory planning is formulated as an optimal control problem, where constraints concerning safety and actuator physical limits are explicitly considered. The results show that, by exploring torque vectoring, the most advanced planner (with the Pacejka tyre model and load transfer) outperformed the others with higher passing velocities and safer trajectories. Moreover, torque vectoring contributed to more consistent passing velocities during trajectory planning and tracking as well as safer trajectories, even with a simpler Dugoff tyre model. Furthermore, the two planners that do not consider torque vectoring had inconsistent or lower passing velocities and less safe trajectories.