Coherent detection has higher receiver sensitivity and linearity, but higher power consumption compared with direct detection. In passive optical network (PON), the cost-effective and low-complexity coherent detection has drawn more and more attention. In this letter, enhanced direct detection least mean square (DD-LMS) and modified constant modulus algorithm (MCMA) schemes are compared in 25/30Gbaud polarization division multiplexing (PDM) four pulse amplitude modulation (PAM4) heterodyne coherent detection PON. Both schemes are used for polarization demultiplexing. With lower computational complexity, enhanced DD-LMS scheme gets better performance compared with MCMA scheme. According to the simulation results, after 80-km transmission, the receiver sensitivity at HD-FEC threshold of 3.8xl0^-3is -33.8dBm and - 32.8dBm for enhanced DD-LMS and MCMA, respectively. The maximum power budgets are 39.2dB and 38.3dB.