From a permeability and selectivity perspective, supported thin-film Pd–Ag membranes are the best candidates for high-purity hydrogen recovery for methane-hydrogen mixtures from the natural gas grid. However, the high hydrogen flux also results in induced bulk-to-membrane mass transfer limitations (concentration polarization) especially when working at low hydrogen concentration and high pressure, which further reduces the hydrogen permeance in the presence of mixtures. Additionally, Pd is a precious metal and its price is lately increasing dramatically. The use of inexpensive CMSM could become a promising alternative. In this manuscript, a detailed comparison between these two membrane technologies, operating under the same working pressure and mixtures, is presented. First, the permeation properties of CMSM and Pd–Ag membranes are compared in terms of permeance and purity, and subsequently, making use of this experimental investigation, an economic evaluation including capital and variable costs has been performed for a separation system to recover 25 kg/day of hydrogen from a methane-hydrogen mixture. To widen the perspective, also a sensitivity analysis by changing the pressure difference, membrane lifetime, membrane support cost and cost of Pd/Ag membrane recovery has been considered. The results show that at high pressure the use of CMSM is to more economic than the Pd-based membranes at the same recovery and similar purity.