How changes in the different steps of protein synthesis—transcription, translation and degradation—contribute to differences of protein abundance among genes is not fully understood. There is however accumulating evidence that transcriptional divergence might have a prominent role. Here, we show that yeast paralogous genes are more divergent in transcription than in translation. We explore two causal mechanisms for this predominance of transcriptional divergence: an evolutionary trade-off between the precision and economy of gene expression and a larger mutational target size for transcription. Performing simulations within a minimal model of post-duplication evolution, we find that both mechanisms are consistent with the observed divergence patterns. We also investigate how additional properties of the effects of mutations on gene expression, such as their asymmetry and correlation across levels of regulation, can shape the evolution of paralogs. Our results highlight the importance of fully characterizing the distributions of mutational effects on transcription and translation. They also show how general trade-offs in cellular processes and mutation bias can have far-reaching evolutionary impacts.