The cobalt tetraphenyl porphyrin (CoTPP) molecule and its adsorption on clean Cu and Ag surfaces are comparatively analyzed within the Density Functional Theory (DFT) framework. Different sets of exchange-correlation functionals — the Local Density Approximation (LDA) and the Gradient Generalized Approximation (along with the PBE functional and the semi-empirical Grimme's corrections of dispersion) — are compared. Two prominent structural adsorption properties are disclosed in all sets of calculations: an asymmetric saddle deformation of CoTPP with an enhanced tilting of the upwards bent pyrroles and a single adsorption site where the Co center occupies a bridge position and one molecular axis (along the direction of the lowered pair of opposite pyrroles) is aligned with the dense-packed substrate direction. The similarities between Cu(111) and Ag(111) surfaces extend to the interfacial electronic structure with similar electronic redistribution and molecular charging. However subtle differences between the two substrates are revealed with bias-dependent STM simulations, especially in the low-bias imaging range. The STM calculations underline the difficulty for the commonly used GGA + D2 DFT framework to quantitatively predict the energy positions of the frontier molecular orbitals (MOs).