Single unidirectional photorefractive ring resonator (SUPRR) and coupled unidirectional photorefractive ring resonator (CUPRR) were considered with BaTiO3 and LiNbO3 crystals as inter-cavity photorefractive media. The relative oscillation intensity and oscillation frequency shift of two SUPRRs with BaTiO3 and LiNbO3 crystals in their cavities, and four CUPRRs with BaTiO3-BaTiO3, LiNbO3-LiNbO3, BaTiO3-LiNbO3 and LiNbO3-BaTiO3 combinations were analysed relative to cavity detuning parameters and compared the oscillation performance of SUPRR with that of CUPRR. In SUPRR, maximum value of relative oscillation intensity is found for BaTiO3 as compared to that of LiNbO3 for zero cavity detuning. In CUPRR, the oscillation intensity in secondary cavity increases with increasing cavities detuning whereas in primary cavity it decreases with increasing cavities detuning. Major finding of this study is that the BaTiO3-LiNbO3 combination of the coupled system provides the highest relative oscillation intensity.