As the share of variable renewable energies in the power system increases, so does the need for flexibility options. These include, inter alia, energy storage, network optimization and expansion, and demand side management. In this paper, a broad sensitivity analysis is carried out to assess the potential role of innovative electrical energy storage technologies in comparison to well-established ones. The innovative technologies considered include compressed heat energy storage, adiabatic compressed air energy storage, power-to-heat-to-power storage, and reversible solid oxide fuel cells storage. To this aim, the cost-optimizing energy system model REMix has been applied to analyze the impact of main techno-economic parameters of electrical energy storages on their role in the future European power supply system. Two main studies have been calculated. The first one deals with a cost sensitivity analysis on a generic storage technology. Among the main findings is that -beside cost -the ratio between photovoltaics and wind power potentials in a particular region have a relevant impact on the capacity as well as on the energy to power ratio of the installed storages. In addition, a strong competition has been observed between energy storages and gas turbines. The second scenario evaluates the competition between well-established and innovative energy storage technologies. The results show that while some of the regions -namely southern Europe, alpine regions and Scandinavia -mainly rely on pumped hydro storage, in most of Central European regions and United Kingdom the cost optimal solution consists of a mix of pumped hydro storage (totaling 64.2 TWh/y of discharged energy in Europe), hydrogen underground storage (45.1 TWh/y) and batteries (27.1 TWh/y), with an additional small share of power-to-heat-to-power storages (0.1 TWh/y). In line with earlier studies, hydrogen storage is found mostly in regions with high wind power supply, while the distribution of batteries is more spread overall in Europe. The model results underline the high sensitivity of the economic efficiency of storage facilities to the investment costs and their components.