Two kinds of slit pore carbon materials, namely activated carbon (AC) and 3D graphene materials (3D-GS), were purchased to examine their methane storage capabilities. The structural analysis and characterization of AC and 3D-GS were carried out using X-ray diffraction (XRD), scanning electron microscopy (SEM), the X-ray energy dispersive spectrum (EDS), and N2 adsorption/desorption isotherms. Additionally, a thermodynamic framework was employed in the Henry’s law region to evaluate the potential well between the adsorbed fluid and adsorbent. The adsorption behavior of methane on two materials at room temperature and high pressure was also investigated. The results show that the Toth equation is the most suitable model for predicting adsorption isotherms than the Langmuir and L-F equations and determines that the absolute uptake of methane storage on AC and 3D-GS are, respectively, 7.86 mmol·g−1 and 8.9 mmol·g−1 at 298 K and 35 bar. In the Henry’s law region, the isosteric heat of methane adsorption on 3D-GS is larger than that of AC. Meanwhile, the potential well between methane and carbon-based materials decreases as the temperature increases. This indicates that the capacity of methane uptake is enhanced at lower temperatures, which is consistent with the measurements of adsorption isotherms. The research concludes that the 3D-GS is more suitable as a material storage medium than AC. This study provides valuable theoretical guidance for exploring the potential of methane storage on slit pore carbon-based material.