We compared global patterns of gene expression between two bird species, the chicken and zebra finch, with regard to sex bias of autosomal versus Z chromosome genes, dosage compensation, and evolution of sex bias. Both species appear to lack a Z chromosome-wide mechanism of dosage compensation, because both have a similar pattern of significantly higher expression of Z genes in males relative to females. Unlike the chicken Z chromosome, which has female-specific expression of the noncoding RNA MHM (male hypermethylated) and acetylation of histone 4 lysine 16 (H4K16) near MHM, the zebra finch Z chromosome appears to lack the MHM sequence and acetylation of H4K16. The zebra finch also does not show the reduced male-to-female (M:F) ratio of gene expression near MHM similar to that found in the chicken. Although the M:F ratios of Z chromosome gene expression are similar across tissues and ages within each species, they differ between the two species. Z genes showing the greatest species difference in M:F ratio were concentrated near the MHM region of the chicken Z chromosome. This study shows that the zebra finch differs from the chicken because it lacks a specialized region of greater dosage compensation along the Z chromosome, and shows other differences in sex bias. These patterns suggest that different avian taxa may have evolved specific compensatory mechanisms.