The purpose of this paper is to present the results of a feasibility study of the supply of electricity and heat to a large user (i.e., a public hospital in Northern Italy) by means of a molten carbonate fuel cell (MCFC) hybrid system in comparison with other technologies. The study investigated three alternative options in order to meet the user’s demand: internal combustion engine, gas turbine, and a hybrid system (molten carbonate fuel cells and gas turbine, MCFC-HS), which is currently under development by Ansaldo Fuel Cell Ltd. and ENEA. The user requirement was the yearly supplies of and . Due to demand fluctuations over the year, integration by electric grid and/or additional thermal boilers was also required and investigated. The approach integrates the usual mass balance with large scale material flow accounting, embodied energy analysis, exergy efficiency, and emergy synthesis, within a LCA perspective. Results show that the best performance from the point of view of energy and exergy efficiency is shown by the MCFC-hybrid system. The latter is also characterized by the lowest embodied energy demand and cumulative material demand as well as by the lowest requirement for direct and indirect environmental support (emergy method). However, the small thermal energy supply of the MCFC-HS compared with the large thermal needs of the hospital calls for a larger use of the additional boiler. The latter device worsens the local-scale emissions of the system, compared with the other alternatives investigated. Results point out that a proper choice cannot only be based on the individual performance of an even well performing technological device, but also needs to be tailored on the system’s characteristics and dynamics, in order to adequately match supply and demand.