We combine x-ray absorption spectroscopy (XAS), x-raymagnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD) data with first principles density functional theory (DFT) calculations and amultiorbital many-body Hamiltonian approach to understand the electronic and magnetic properties of Co atoms adsorbed on h-BN/Ru(0001) and h-BN/Ir(111). The XAS line shape reveals, for both substrates, an electronic configuration close to 3d(8), corresponding to a spin S = 1 Magnetic field dependent XMCD data show large (14 meV) out-of-plane anisotropy on h-BN/Ru(0001), while it is almost isotropic (tens of mu eV) on h-BN/Ir(111). XMLD data together with both DFT calculations and the results of the multiorbital Hubbard model suggest that the dissimilar magnetic anisotropy originates from different Co adsorption sites, namely atop Non h-BN/Ru(0001) and 6-fold hollow on h-BN/Ir(111).