In this study, the adsorption mechanisms and interactions between the anticancer molecule Crizotinib (CZT) on the surfaces of carbon nanotubes (CNTs) and boron nitride nanotubes (BNNTs) are investigated. The investigations are carried out using the density functional theory (DFT) and the conductor-like screening model for real solvents (COSMO-RS). The quantum molecular descriptors (QMD) are also computed to explain the drug-carrier interaction mechanism and energy of adsorption. The negative adsorption energies of the complex drug-CNT indicate that adsorption is exothermic. The electrophilicity index of the drug-CNT system is five times greater than that of the drug-BNNT, demonstrating the higher stability of the CNTs with respect to BNNT. Moreover, a stronger interaction is observed for CZT-CNT, using the COSMO-RS method. A solvation study in water also reveals that the CZT-CNT complex is more soluble than CZT-BNNT. Finally, a quantum theory of atoms in molecules (QTAIM) analysis is also applied to investigate the nature of the intermolecular interactions. Based on the obtained results, it can be concluded that CNTs are more stable and better carriers than BNNTs when applied for CZT drug delivery in biological media.