Electrochemical surface-enhanced hyper-Raman scattering (SEHRS) and surface-enhanced Raman scattering (SERS) of centrosymmetric molecules on Ag film over nanosphere (AgFON) electrodes are presented. The SEHR spectra of trans-1,2-bis(4-pyridyl) ethylene (BPE) at different potentials (vs Ag/AgCl) are presented for the first time, and a reversible potential tuning of the SEHR spectra of BPE is demonstrated. The SEHRS and SERS techniques were used to determine to what extent either site symmetry reduction or field gradient effects dictate the origin of the observed vibrational spectra. It is found that the SEHR and SER spectra for the molecules studied were distinctly different at all frequency regions at a fixed voltage, suggesting that centrosymmetry is largely retained upon adsorption to the AgFON surface and that field gradient effects are negligible. This work also shows that the SEHR spectra clearly depend on potential, whereas the SER spectra are essentially independent of potenial. It is determined that the combination of changes in Delta G(ads) and the presence of coadsorbed counterions are responsible for altering the local symmetry of the adsorbate and only SEHRS has the sensitivity to detect these changes in the surface environment. Thus, SEHRS is a uniquely useful spectroscopic tool that is much more sensitive to the local adsorption environment than is SERS.