For nanostructured interfaces between open-shell molecules and metal surfaces that involve charge transfer upon adsorption, the investigation of molecular magnetic properties is an interesting yet difficult task, because in principle different magnetic configurations with distinct properties can be found. Here, we study the magnetic properties of CuPc-Ag and CoPc-Ag interfaces, which constitute interesting test cases because charge is transferred to the initially open-shell Pc molecules upon adsorption. Using hybrid density functional theory, we examine the stability of the various magnetic configurations occurring at these nanoscale interfaces, as well as for the corresponding gas-phase anions, and compare our findings to those of previous experimental studies. For CuPc-Ag, we identify a high-spin triplet configuration as the most likely configuration at the interface, whereas for CoPc-Ag a quenching of the total magnetic moment is found. Interestingly, such quenching is consistent with two distinctly different interfacial electronic configurations. These important differences in the magnetic properties of CuPc and CoPc on Ag are rationalized by variations in the interaction of their central metal atoms with the substrate. Our work facilitates a deeper understanding of the magnetic configuration and interlinked electronic-structure properties of molecule-metal interfaces. Furthermore, it highlights the necessity of an appropriate choice of methodology in tandem with a detailed evaluation of the different emerging magnetic properties.