Face recognition and verification are two computer vision tasks whose performance has progressed with the introduction of deep representations. However, ethical, legal, and technical challenges due to the sensitive character of face data and biases in real training datasets hinder their development. Generative AI addresses privacy by creating fictitious identities, but fairness problems persist. We promote fairness by introducing a demographic attributes balancing mechanism in generated training datasets. We experiment with an existing real dataset, three generated training datasets, and the balanced versions of a diffusion-based dataset. We propose a comprehensive evaluation that considers accuracy and fairness equally and includes a rigorous regression-based statistical analysis of attributes. The analysis shows that balancing reduces demographic unfairness. Also, a performance gap persists despite generation becoming more accurate with time. The proposed balancing method and comprehensive verification evaluation promote fairer and transparent face recognition and verification.