Joint pilot and data power control (JPDPC) is known to have a large impact on both the overall spectral/energy efficiency and fairness of cell-based systems. However, the impact of JPDPC on the inherent spectral/energy efficiency and fairness trade-off in cell-free (CF) systems is much less understood. In this letter, considering pilot contamination, user-centric clustering and multi-antenna access points, we formulate novel JPDPC problems in CF systems as distinct optimization tasks, whose objectives are maximizing the minimum spectral efficiency (SE), maximizing the total SE and maximizing the product of the individual signal-to-interference-plus-noise ratios. Since these problems are non-convex, we solve them by combining successive convex approximation and geometric programming. To the best of our knowledge, this is the first letter analyzing and optimizing JPDPC in user-centric CF systems. Our results indicate that JPDPC allows users to save more energy than the disjoint optimization of pilot and data powers when maximizing the minimum SE, while showing that JPDPC plays a crucial role in balancing between SE and fairness also in CF systems.