The fact that the average DC component on both encodings is zero is very desirable: no energy is lost in the carrier, meaning the entirety of the energy used in these standards is used to represent data. This also means that there’s no extra noise.
Perhaps the most relevant difference is how the information is transmitted. In the case of Manchester, the polarity of the bit at a given time determines the symbol, while in BMC it’s the transition at the middle of the bit-time (or lack-there-of) that determines whether we have a 1 or a 0. The latter is much more desirable because it adds an extra protection layer against noise, and also facilitates its use in differential signals. This shouldn’t come as a surprise, as one of its alternate names is Manchester Differential encoding. In a nut-shell, BMC is much more robust than simple Manchester encoding.