Herein, the nanoconfinement of LiBH4 and NaBH4 in a carbon (carbon nanotubes, MBH4@CNT) and an inorganic support (CuS hollow nanospheres, MBH4@CuS) is compared. Both led to drastic improvements in hydrogen storage properties, with hydrogen desorption occurring from room temperature, and the reversibility greatly enhanced. However, successive hydrogen desorption and absorption cycles for MBH4@CNT led to a decrease in hydrogen storage capacity, most likely due to partial oxidation from oxygen-containing groups on the surface of the carbon nanotubes. In contrast, little to no decrease in capacity was observed for MBH4@CuS, indicating that similar materials may be a more viable alternative for future nanoconfinement research.