We investigated the effect of the free-layer composition and the pattern size of magnetic cell on current-induced magnetization switching in asymmetric MgO-based magnetic tunnel junctions. We found that the normalized switching phase diagrams (SPDs) measured at low temperature are mostly determined by the material composition of ferromagnetic electrodes but are not much sensitive to the intrinsic energy barrier and the anisotropy field of the sample. This experimental result indicates that the normalized SPD can be used to study the fundamental characteristics of spin-transfer torque.