The transition of the energy system to renewable sources means the cheap energy storage in fossil fuels must be replaced by other options. A large part of the demand for useful energy is heat and cold, often produced from electric energy by a resistance heater, compression heat pump or cooler. The question is then to store the initial electric energy by electric energy storage (EES) or the useful energy by thermal energy storage (TES). In a desktop study both options were compared, by the choice made in existing applications, and also generally analyzing current technology data. For the latter, cost, round-trip efficiencies, life cycles and life time of EES, specifically for batteries, and of TES, specifically for hot and cold water, ice and other PCM were collected. Applications studied are heating and cooling in buildings and in industry. Application-typical conversion efficiencies were also collected and taken into account. The results show that in many existing installations TES, incl. by PCM, is already preferred, and that TES is advantageous in most investigated applications economically, in addition to technical advantages. Thus, TES has a large potential in the transition of the energy system to stabilize the electricity grid by demand side management.