Anion photoelectron spectroscopy and quantum chemical calculations at the density functional theory (DFT), coupled cluster theory (CCSD(T)), and complete active space self-consistent field (CASSCF) theory levels are employed to study the reduced transition metal oxide clusters M4O10- (M = Cr, W) and their neutrals. Photoelectron spectra are obtained at 193 and 157 nm photon energies, revealing very different electronic structures for the Cr versus W oxide clusters. The electron affinity and HOMO-LUMO gap are measured to be 3.68 +/- 0.05 and 0.7 eV, respectively, for the Cr4O10 neutral cluster, as compared to 4.41 +/- 0.04 and 1.3 eV for W4O10. A comprehensive search is performed to determine the ground-state structures for M4O10 and M4O10-, in terms of geometry and electronic states by carefully examining the calculated relative energies at the DFT, CCSD(T), and CASSCF levels. The ground states of Cr4O10 and Cr4O10- have tetrahedral structures similar to that of P4O10 with the anion having a lower symmetry due to a Jahn-Teller distortion. The ground states of W4O10 and W4O10- have butterfly shape structures, featuring two fused five-member rings with a metal-metal multiple bond between the central metal atoms. The much stronger WW bonding than the CrCr bonding is found to be the primary cause for the different ground state structures of the reduced Cr4O100/- versus W4O100/- oxide clusters. The photoelectron spectra are assigned by comparing the experimental and theoretical adiabatic and vertical electron detachment energies, further confirming the determination of the ground electronic states of M4O10 and M4O10-. The time-dependent DFT method is used to calculate the excitation energies of M4O10. The TD-DFT results in combination with the self-consistently calculated vertical detachment energies for some of the excited states at the DFT and CCSD(T) levels are used to assign the higher energy bands. Accurate clustering energies and heats of formation of M4O10 are calculated and used to calculate accurate reaction energies for the reduction of M4O12 to M4O10 by CH3OH, as well as for the oxidation of M4O10 to M4O12 by O-2. The performance of the DFT method with the B3LYP and BP86 functionals in the calculations of the relative energies, electron detachment energies, and excitation energies are evaluated, and the BP86 functional is found to give superior results for most of these energetic properties.