Ultrabright sources of entangled photon pairs with high heralding efficiency are an important step in the pursuit of high-bit-rate entanglement-base quantum key distribution, as well as an enabling tool for loss-sensitive quantum optics experiments. Here, we present a robust single-mode fiber-coupled source of polarization-entangled photons around 810 nm with both high brightness and heralding efficiency. Our approach is based on quasi-phase-matched spontaneous parametric downconversion (SPDC) from periodically poled KTiOPO4 in a Sagnac loop configuration. We demonstrate a high degree of two-photon polarization entanglement for single-frequency-pumped type-0 and type-II SPDC, and conduct a conclusive comparison in terms of efficiency and spectral characteristics. In light of applications outside a laboratory environment, we evaluate the feasibility of pumping nonlinear crystals with free-running laser diodes.