Structurally similar transition metal systems can have widely differing magnetic properties. A prime example of this is found for bilayers on Ir(111), where Pd/Fe/Ir(111) ground state has a wellestablished noncollinear spin texture, while Pd/Co/Ir(111) present a ferromagnetic (FM) singledomain. To unravel the origins of these different magnetic behaviors, an investigation of Pd/Fe and Pd/Co bilayers on Ir(111), is here performed. Based on the obtained ab-initio electronic structure, exchange coupling parameters (Jij) and Dzyaloshinskii-Moriya interactions (DMI), we demonstrate that, although in Pd/Co/Ir(111) the DMI is significant, two ingredients play a key role on the origin of noncollinearity in Pd/Fe/Ir(111): the presence of magnetic frustrations and a much more in-plane DMI, both with a long-range influence. The Jij and DMI behaviors in both systems can be explained in terms of a simple rigid-band-like model. Also, by performing spin-dynamics simulations with the magnetic parameters tuned from the Pd/Co/Ir(111) to Pd/Fe/Ir(111) ab-initio values, we could find conditions for the emergence of skyrmionic phases in the originally FM Pd/Co/Ir(111).