The growth of Ga₂O₃ films by halide vapor phase epitaxy on plain and cone-shaped patterned sapphire substrates (PSS) is reported. The obtained specimens are characterized by X-ray diffraction, transmission electron microscopy, cathodoluminescence, optical transmission spectroscopy, and current–voltage measurements. Both types of Ga₂O₃ layers are of reasonably high crystal qualities; their physical properties, however, are very different. Under the same conditions, the growth on plain substrates results in a continuous α-Ga₂O₃ layer, whereas the growth on PSS produces a regular array of α-Ga₂O₃ columns on top of the sapphire cones with the space between them filled with ε-Ga₂O₃. Ga₂O₃ films grown on plain sapphire are insulating; in contrast, Ga₂O₃ films grown on PSS are conducting. It is found that the conductivity of Ga₂O₃ on PSS follows the Arrhenius law with the activation energy of 0.33 eV. New luminescent bands for α- and ε-phases are found. Spectral components of the defect-related luminescence for α- and ε- phases are identified.