In this paper we investigate the effect of disorder on highly correlated electron systems, which exhibit metal-insulator transition (MIT) and structural-phase transition (SPT). We show that the effect of ion irradiation is strikingly different between ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ and $\mathrm{V}{\mathrm{O}}_{2}$, two otherwise similar materials. Upon irradiation, the MIT and SPT temperatures in ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ decrease drastically at low absolute dosages, much lower than for $\mathrm{V}{\mathrm{O}}_{2}$. At a low threshold dose, the insulating state of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ drastically collapses into a metallic state. Contrary to this, irradiation of $\mathrm{V}{\mathrm{O}}_{2}$ leads to a much milder reduction of the MIT and SPT temperatures and to a weak, gradual decrease of the insulating state resistivity---not suppressed even at one order of magnitude higher doses than the ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ threshold. These major differences imply that the phase transition in ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ arises from global (rather than local as in $\mathrm{V}{\mathrm{O}}_{2}$) physical mechanisms that are extremely sensitive to disorder. This shows that the MIT and SPT may have substantially different physical origins in different systems, with the consequent major implications for theoretical descriptions of the MIT in highly correlated electron systems.