Performance of the thermally-driven metal hydride hydrogen compressor (MHHC) is defined by (a) its H2 compression ratio and maximum output H2 pressure; (b) throughput productivity/average output flow rate; (c) specific thermal energy consumption which determines H2 compression efficiency. In earlier studies, the focus of the R&D efforts was on the optimisation of the design of the MH containers and heat and mass transfer in the MH storage and compression system aimed at shortening the time of the H2 compression cycle. This work considers an important but insufficiently studied aspect of the development of the industrial-scale thermally driven MHHC's – selection of the materials and optimisation of the materials performance. Further to the operation in the specified pressure/temperature ranges, materials selection should be based on the estimation of the productivity of the compression cycle, and specific heat consumption required for the H2 compression, which together determine the process efficiency. The current work presents a model to determine productivity and heat consumption for a single- and multi-stage MHHC's which is based on use of Pressure – Composition – Temperature (PCT) diagrams of the utilized metal hydrides at defined operating conditions – temperatures and hydrogen pressures – and main operational features of the MHHC (number of stages, amounts of the MH materials used, cycle time). In Part I of this work [Lototskyy, Yartys, et al., Int J Hydrogen Energy, DOI: 10.1016/j.ijhydene.2020.10.090], we showed that the calculated cycle productivities significantly vary for the different materials. Analysis of the system performance carried out in this work (Part II) shows that the throughput productivity and efficiency of a multi-stage MHHC also depends on the types and amounts of the used MH materials in the multi-stage compressor layout. This has been analysed for a number of the most practically important AB5 and Laves type AB2 hydrogen storage alloys integrated into the MHHC's. A comparison of experimentally measured performances of single-, two- and three-stage industrial-scale MHHC's developed by the authors earlier shows their satisfactory agreement with the modelling results thus demonstrating a high value of the presented method for the proper materials selection during development of the MHHC. As an important future development, the work presents a performance evaluation of a two-stage MHHC for H2 compression operating in the pressure range from 30 to 500 atm at operating temperatures between 20 and 150 °C.