The electronic structure of two recently crystallographically solved, thiolate-phosphine protected silver clusters Ag-14 and Ag-16 are analyzed via density functional theory (DFT) and their optical excitations are analyzed from time-dependent DFT perturbation theory. Both clusters can be characterized as having the S-2 free-electron configuration in the metal core, which is the first time such a configuration is confirmed for structurally known ligand-protected noble metal clusters. However, their different core shapes and ligand layer induce significantly different optical spectra. Performance of gradient-corrected DFT functionals is discussed and it is shown that the asymptotically correct Leeuwen-Baerends LB94 functional reproduces the optical spectrum of Ag-14 in a good agreement with experiment. Choice of the functional becomes important for clusters where the optical transitions are dominated by the electron-rich ligand layer.