Solid-state batteries are promising for electric mobility as they potentially offer higher energy densities and therefore driving range, long-life and safety. They come with changed thermal properties and thermal management requirements. In this paper a comparison of a solid-state battery system with a state-of-the-art liquid battery system is presented. This study compares a solid-state battery with a state-of-the-art liquid NMC battery for an electric coach on typical real-world long-distance routes, including fast-charging. The thermal management is performed by a reversible R744 heat pump. By designing both battery systems for the same energy capacity, the solid-state battery releases more heat during fast-charging. At the same battery system size, the solid-state battery significantly outperforms the liquid battery system in driving range and does not need more cooling.