The formation of a hydride from a metal or intermetallic alloy is an exothermic reversible chemical reaction. The thermodynamic properties governing hydride formation facilitate their thermochemical applications, such as hydrogen compression. Thermal transport inside the materials is of highest importance for system dynamics and its productivity. In this contribution, we demonstrate a two-stage thermochemical hydrogen compressor using the AB₅ alloy LaNi₅ in the first stage and an AB₂ alloy TiMn₂ (Hydralloy®) in the second stage. To evaluate the impact of the thermal conductivity of the materials, the productivity of the compressor was compared for pure metal hydride compacts (MH) and metal hydride composite materials (MHC). Compared to pure MH pellets, the MHC used in this study contain expanded natural graphite (ENG), a secondary phase with highest thermal conductivity. As the radial thermal conductivity of the MHC increased, the time required for the loading, temperature change and unloading steps was successfully reduced by 400%. Productivity was increased by over 320 % from 14 Nl_H2/(kg_Material*h) to 44 Nl_H2/(kg_Material*h). Overall, MHC have the potential to simplify handling, reactor design and reduce investment costs for thermochemical compression systems. Thus, MHC have highest impact and potential for thermochemical applications.