In this study, the storage capacities of new-concept metal organic frameworks (MOFs) hybrids towards CO2 and CH4 were investigated. Three benzene-1,3,5-tricarboxylic acid (BTC)-based MOFs with different metallic centers (Cu, Al, Fe) and their hybrids embedding a new-concept graphene related material (graphene like (GL) layers) at low concentration (5 wt%) were produced. Adsorption/desorption tests have been carried out at room temperature (RT) up to 5.0 MPa depending on the gas specimen and the adsorption data have been modeled in accordance with the Töth model. All the sorbents exhibited a higher affinity toward CO2 over CH4. The MOF/GL hybrids and the pristine MOFs exhibited reversible adsorption process with and/or without regeneration through thermal treatment. In particular, the Cu- and Fe-based MOFs fully recovered their CO2 storage capacity without any thermal treatment. MOF/GL hybrids exhibited a quicker saturation for all the analyzed gases. The MOF/GL hybrids and the pristine MOFs presented similar interaction with the tested gases: the occurrence of strong interactions (nearing the magnitude of chemisorption) is evidenced for Cu-based and Al-based materials, while physisorption phenomena characterized the Fe-based materials. The selectivity towards CO2 over CH4 exhibited by MOF/GL hybrids appeared interesting (over 65 in the case of the Cu-based hybrid), even if great advantages over that of the pristine MOF at high pressure were not detected for all the investigated materials. Finally, it is worth noting the enhanced CO2 and CH4 adsorptions exhibited at low-pressure (<0.2 MPa) by the Al-based hybrid.