Anharmonic vibrational spectroscopy calculations using MP2 and B3LYP computed potential surfaces are carried out for a series of molecules, and frequencies and intensities are compared with those from experiment. The vibrational self-consistent field with second-order perturbation correction (VSCF-PT2) is used in computing the spectra. The test calculations have been performed for the molecules HNO3, C2H4, C2H4O, H2SO4, CH3COOH, glycine, and alanine. Both MP2 and B3LYP give results in good accord with experimental frequencies, though, on the whole, MP2 gives very slightly better agreement. A statistical analysis of deviations in frequencies from experiment is carried out that gives interesting insights. The most probable percentage deviation from experimental frequencies is about -2% (to the red of the experiment) for B3LYP and +2% (to the blue of the experiment) for MP2. There is a higher probability for relatively large percentage deviations when B3LYP is used. The calculated intensities are also found to be in good accord with experiment, but the percentage deviations are much larger than those for frequencies. The results show that both MP2 and B3LYP potentials, used in VSCF-PT2 calculations, account well for anharmonic effects in the spectroscopy of molecules of the types considered.