Fast electric vehicle (EV) charging stations often face limitations related to restricted grid connection capacity. To overcome these constraints, battery energy storage systems (BESS) are increasingly integrated to support charging demand while providing ancillary services such as peak shaving and energy arbitrage. However, most installations rely on monotype BESS solutions, which may not fully exploit the different power and energy requirements of these services. This paper investigates the use of a hybrid battery energy storage system (HBESS) combining high-energy (HE) and high-power (HP) battery technologies in a fast EV charging station. The study is based on a real charging station under development in Norway and considers realistic operating conditions, including measured charging demand profiles, electricity market prices, and local tariff structures. Three storage configurations are evaluated: (i) an HBESS composed of second-life NMC modules as the HE subsystem and LTO modules as the HP subsystem, (ii) a monotype BESS based solely on second-life NMC modules, and (iii) a monotype BESS based solely on LTO modules. The charging station operation is simulated in Matlab environment using coordinated energy management and power management strategies that simultaneously perform energy arbitrage and peak shaving. Technical and economic performance indicators, including electricity cost savings, peak demand reduction, grid utilization, losses, and payback time, are evaluated. The results provide insights into the potential benefits of HBESS solutions for future EV charging stations and support storage system sizing and planning in applications with both energy- and power-intensive requirements.