The electronic structure of YBa2Cu3O6+x and La2-xSrxCuO4 for various values of x has been investigated using hard x-ray photoemission spectroscopy. The experimental results establish that the cleaving of YBa2Cu3O6+x compounds occurs predominantly in the BaCuO3 complex leading to charged surfaces at higher x and to uncharged surfaces at lower x values. The bulk component of the core level spectra exhibits a shift in binding energy as a function of x, from which a shift of the chemical potential as a function of hole concentration in the CuO2 layers could be derived. The doping dependence of the chemical potential across the transition from a Mott-Hubbard insulator to a Fermi-liquid-like metal is very different in these two series of compounds. In agreement with previous studies in the literature the chemical potential shift in La2-xSrxCuO4 is close to zero for small hole concentrations. In YBa2Cu3O6+x, similar to all other doped cuprates studied so far, a strong shift of the chemical potential at low hole doping is detected. However, the results for the inverse charge susceptibility at small x shows a large variation between different doped cuprates. The results are discussed in view of various theoretical models. None of these models turns out to be satisfactory. ; Comment: 18 pages, 15 figures