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They should resemble each other if both sexes have only a single chromosome with barring gene but both breeds are supposed to fixed for barring gene on Z-chromosome . Therefore, in this case of dominque crossed with California grey, if cross is male there should be 2 copies of barring allele and if female 1 copy. Henk. it was you that noted the male and female versions of cross can not be differentiated. I agree they can not be differentiated like similar aged pure American dominique or California grey. Females should appear much darker.
Either some modifier is at play or another loci codes for barring. I am guessing latter since dark and lite bars are of similar width in both sexes. If latter so then couple possibilities exists, second loci for barring on z-chromosome or it is autosomal.