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Experimental data for 140, 142Се and 153Eu nuclei are analyzed jointly using the cross sections for total and partial photoneutron reactions obtained with quasimonoenergy photon beams formed during the annihilation of relativistic positrons. The results from an experiment performed on a bremsstrahlung beam are also used for such an analysis for the 153Eu nucleus. Well-known systemic discrepancies between the results of different experiments are analyzed using the objective physical criteria of data reliability, and ways of allowing for them are considered. New data on the cross sections of (γ, 1n) and (γ, 2n) reactions for 140, 142Се nuclei, on the cross section of (γ, 3n) reaction for 153Eu nucleus, and on the cross section of total photoneutron reaction for all three nuclei were obtained additionally the cross sections of partial reactions that satisfy the established criteria of reliability. It was shown that substantial deviations of the experimental reaction cross sections from those evaluated are due to an unreliable sorting of neutrons between the channels with a multiplicity of 1, 2 due to the abovementioned systematic uncertainties. [ABSTRACT FROM AUTHOR]