The balanced output is based on relative efficiency of the woofers vs. midpanels and tweeter. However, the crossover can also be designed to pad the output of the more efficient section to keep the output the same.
I am bi-wiring and the output seems about the same. IMO, the key to successful bi-amping is matching the input sensitivity of the two amplifiers. Some amps need only 1V to reach full output, others need more or less, which can cause differences in output which could be good or bad depending on how much power goes where.