Which of the following statements is correct?

In $\mathrm{B}\mathrm{C}{\mathrm{l}}_3,\mathrm{p}\mathrm{\pi }-\mathrm{p}\mathrm{\pi }$ back-donation occurs between the vacant 2p-orbital of 'B' and fully-filled 3p-orbital of Cl of a $\mathrm{B}-\mathrm{C}\mathrm{l}$ bond. This $\mathrm{p}\mathrm{\pi }-\mathrm{p}\mathrm{\pi }$ overlapping is not much effective, because of dissimilar sizes of 2p and 3p-orbitals. But in $\mathrm{A}\mathrm{l}\mathrm{C}{\mathrm{l}}_3$ , $\mathrm{p}\mathrm{\pi }-\mathrm{p}\mathrm{\pi }$ overlapping is more effective, because p-orbitals of Al and Cl belongs to the same energy levels and hence, they are of similar sizes. As a result of back-donation, the electron-deficiency of Al atom gets more compensated as compared with 'B' in $\mathrm{B}\mathrm{C}{\mathrm{l}}_3$ and therefore, Lewis acid character of $\mathrm{A}\mathrm{l}\mathrm{C}{\mathrm{l}}_3$ is lesser than that of $\mathrm{B}\mathrm{C}{\mathrm{l}}_3$ .