Photon entanglement is at the basis of many protocols in photonic quantum technologies, from quantum computing to simulation and sensing. The generation of entangled photons in integrated waveguides is particularly advantageous due to the enhanced stability and more efficient nonlinear interaction. Here we realize an integrated source of entangled wavelength-degenerate photons based on the hybrid interfacing of photonic circuits in different materials, all inscribed by femtosecond laser pulses. We show that our source, based on spontaneous parametric down-conversion at the telecom wavelength, gives access to different classes of output states, allowing us to switch from path-entangled to polarization-entangled states with net visibilities above 0.92 for all selected combinations of integrated devices.