Low-Density Parity-Check (LDPC) and polar codes are two classes of channel codes potentially able to achieve the channel capacity, and both are used in current 5G communication systems. Belief Propagation (BP), which is the main decoding algorithm for LDPC codes could also be used for decoding polar codes. A fully parallel fully unrolled BP decoding architecture has been recently proposed for both of these codes. In this paper, we investigate these two architectures further and compare the two codes from the viewpoint of Bit-Error Rate (BER) performance, achieved throughput, latency, chip area, and also energy efficiency. Toward that, both architectures have been synthesized in a 28 nm CMOS technology, and corresponding results are provided.