Carbon nanotubes (CNTs) are nanoscale tubes made of carbon atoms with unique mechanical, electrical, and thermal properties. They have a variety of promising applications in electronics, energy storage, and composite materials and are found as single-wall carbon nanotubes (SWCNTs) and double-wall carbon nanotubes (DWCNTs). Considering such alluring attributes of nanotubes, the motive of the presented flow model is to compare the thermal performance of magnetohydrodynamic (MHD) mono (SWCNTs)/Ethylene glycol) and hybrid (DWCNTs- SWCNTs/Ethylene glycol) nanofluids over a bidirectional stretching surface. The thermal efficiency of the proposed model is gauged while considering the effects of Cattaneo-Christov heat flux with prescribed heat flux (PHF) and prescribed surface temperature (PST). The flow is assisted by the anisotropic slip at the boundary of the surface. The system of partial differential equations (PDEs) is converted into a nonlinear ordinary differential system by the use of similarity transformations and handled using the bvp4c numerical technique. To depict the relationship between the profiles and the parameters, graphs, and tables are illustrated. The significant outcome revealed that the fluid temperature rises in the scenario of both PST and PHF cases. In addition, the heat transfer efficiency of the hybrid nanoliquid is far ahead of the nanofluid flow. The truthfulness of the envisioned model in the limiting scenario is also given.