Following the suppression of recombination, gene expression levels decline on the sex-limited chromosome, and this can lead to selection for dosage compensation in the heterogametic sex to rebalance average expression from the X or Z chromosome with average autosomal expression. At the same time, due to their unequal pattern of inheritance in males and females, the sex chromosomes are subject to unbalanced sex-specific selection, which contributes to a nonrandom distribution of sex-biased genes compared to the remainder of the genome. These two forces act against each other, and the relative importance of each is currently unclear. The Gallus gallus Z chromosome provides a useful opportunity to study the importance and trade-offs between sex-specific selection and dosage compensation in shaping the evolution of the genome as it shows incomplete dosage compensation and is also present twice as often in males than females, and therefore predicted to be enriched for male-biased genes. Here, we refine our understanding of the evolution of the avian Z chromosome, and show that multiple strata formed across the chromosome over ∼130 million years. We then use this evolutionary history to examine the relative strength of selection for sex chromosome dosage compensation vs. the cumulative effects of masculinizing selection on gene expression. We find that male-biased expression increases over time, indicating that selection for dosage compensation is relatively less important than masculinizing selection in shaping Z chromosome gene expression.