Transient surface photovoltage (SPV) spectroscopy, optical absorption, and photoconductivity (PC) were applied to study electronic transitions in (-201) β-Ga2O3 and (001) κ-Ga2O3 epitaxial layers on c-plane sapphire substrates. SPV signals were distinguished for charge separation near the surface and near the layer/substrate interface. The bandgaps of β-Ga2O3 and κ-Ga2O3 epitaxial layers were found to be, respectively, about 4.75 and 4.79 eV from optical absorption measurements, about 4.8 and 4.9 eV from PC, and 4.65 and 4.9 (near the surface) from SPV measurements. Near the κ-Ga2O3 layer/substrate interface SPV instead gives a value of 4.75 eV, possibly related to the presence of an interlayer. Defect-related transitions with onset energies at about 4.5, 4.1, and 3.5 eV were observed along the whole β-Ga2O3 layer cross-section. In contrast, defects related to different transitions were differently distributed in κ-Ga2O3 epitaxial layers: transitions setting on at about 4.3 eV originate from defects uniformly distributed across the layer, while transitions starting at 2.4 eV and 1.7 eV were respectively connected with defects located near the surface or near the layer/substrate interface. The PC measurements at photo-excitation energy above the bandgap indicated that defect densities and recombination losses were much larger in κ-Ga2O3 than in β-Ga2O3.