The exploration of future energy system trajectories needs to be based on long-term scenarios, which in turn requires using long-term modelling tools. Introducing a strong decarbonisation constraint, for instance, profoundly modifies the power sector, which is impacted by increasing shares of variable renewable energy sources. Long-term modelling tools working on different assumptions increasingly factor in these impacts, the assessment of which requires a clear description and categorization of the technical and economic choices for representing the tools in question. A new typology based on a literature review is presented for both power sector models and long-term models of the energy system. New comparing criteria focussing on the power sector's components are put forward, such as electricity storage and grid. An analysis carried out by means of this categorization on five chosen models shows that, up until now, energy modelling tools and power system tools have been designed to meet separate objectives and have not combined their advantages.