We explore the potential of versatile and efficient entangled photon pair generation by spontaneous parametric downconversion in Bragg reflection waveguides. By employing a quantum treatment of modes in channel waveguides, and by accounting for group velocity dispersion in the modes, the quantum state of the generated biphotons is realistically calculated. The pair production rate is predicted to reach $4\times {10}^8\text{pairs}/\mathrm{s}/\mathrm{nm}/\mathrm{mW}$ of pump light in a 2 mm-long structure, on par with or exceeding the performance of previously reported designs. This is attributable to an enhanced nonlinear interaction through tight mode confinement in the waveguide. Strategies for device performance optimization and phase matching wavelength tunability are outlined and numerically demonstrated. The proposed design platform is versatile and allows photon pair generation with controllable flux, bandwidth, Schmidt number, and degree of polarization entanglement. The possibility of monolithic integration with a diode laser pump offers a way to design an electrically pumped entangled photon source.