DFT calculations on a 4-ring cluster and on ONIOM models of faujasite were carried out to assess the concept of basicity in zeolites, exchanged with alkali cations. The considered reaction is the methylation of the SiO-Al bridging oxygen by methanol and methyl iodide. The reaction involves both the dissociation of the H3C-OH or H3C-I bonds and the formation of the C-O-zeolite bond. The former involves the hardness of the alkaline cation. The latter reflects the charge density of the basic oxygen, well described by the "hard" descriptor: the molecular electrostatic potential. The harder is the alkali metal, the easier is the H3C-OH or H3C-I bond dissociation, and the lower is the basicity of the bridging oxygen, and thus the more difficult is the C-O-zeolite bond formation. The fact that these two processes compete has been established by comparing the energy profiles for the methylation with methyl iodide and methanol. For methanol the role of the alkaline metal on the bond dissociation prevails because of the larger hardness of the OH group as compared to that of the iodine atom. For methyl iodide the oxygen basicity prevails over the interaction of I with metal. This study clearly shows that in both experimental and theoretical studies the role of the Lewis acidity or hardness of the alkali metal ion and the role of the basicity of the framework oxygen have to be separated from each other for a good interpretation of zeolite basicity. Also, the hardness of the probe molecule is particularly important when considering the interaction with the alkali metal ion.