The influence of rare earth (RE) elements on superconducting properties of the transition element (TE)-substituted TE xCu1- xSr2RECu2O y cuprates has not been sufficiently emphasized so far. In the case of molibdo-cuprates with the general formula Mo0.3Cu0.3Sr2RECu2O y, all the RE element containing compounds except La, Ce, and Lu can be prepared at room pressure. The influence of the crystal structure on the superconducting properties after ozone oxidation of the present system is reported selecting three groups of RE elements attending to their different atom sizes: small (Yb and Tm), medium (Gd), and big (Nd and Pr). Advanced transmission electron microscopy, various diffraction techniques, and spectroscopic analysis have been used to demonstrate that the increase of structural disorder complemented with a decrease in the hole content play a major role in the vanishing of superconductivity within the present system.