Some of the above responses seem to imply that when "passively" biamping (i.e., using two amps on a biwirable speaker with no external line-level crossover added, be that active or passive -- "passive" biamping is actually a misleading/confusing term in that sense!), you don't get the benefits of relieving the upper-frequency amp from having to deal with the bass frequencies. Although passive attenuation (by the speaker's crossover) after the power output isn't exactly the same as filtering out those bass frequencies before feeding the signal to the treble-range power amp in the first place, there is still worthwhile benefit to be gained (at least in theory) by not requiring that amp to drive a woofer. The amp inputs may "see" the full frequency range, but the output section of the HF amp is not being called upon to deliver much current in the LF. This is of course in addition to the other theoretical benefits, like doubling the available amp power (assuming the top and bottom amps are identical).
I've only ever done passive biamping, but my feeling is that the main benefits of "active" biamping (again in theory - in practice, as has been pointed out above, all bets may be off under the wrong circumstances) are mostly in implementing the frequency-divider network at the low-power line level instead of the high-power speaker level. (Which, as was also pointed out above, relieves the power amps from having to deal with the more reactive load of a speaker's crossover -- in addition to eliminating the high power-handling requirement so the crossover can be miniturized, and removing it from the highly vibrational environment inside the speaker cabinet.) My guess is that this factor is much more significant than any benefit gained from restricting the frequency range seen at the power amp inputs per se. After all, to my knowledge no one has postulated a benefit in relieving the system preamp from handling the full frequency range by dividing the signal after the source and using two preamps...
BTW, I also have to disagree about the wisdom of using different and possibly dissimilar amps for the different frequency ranges (subwoofer amps excluded) -- in my (albeit limited ) experience, using identical or very similar amps (and cables) top and bottom is necessary for the sound not to risk becoming discontinuous, at least with speakers that are coherent/consistent top-to-bottom to begin with.
I've only ever done passive biamping, but my feeling is that the main benefits of "active" biamping (again in theory - in practice, as has been pointed out above, all bets may be off under the wrong circumstances) are mostly in implementing the frequency-divider network at the low-power line level instead of the high-power speaker level. (Which, as was also pointed out above, relieves the power amps from having to deal with the more reactive load of a speaker's crossover -- in addition to eliminating the high power-handling requirement so the crossover can be miniturized, and removing it from the highly vibrational environment inside the speaker cabinet.) My guess is that this factor is much more significant than any benefit gained from restricting the frequency range seen at the power amp inputs per se. After all, to my knowledge no one has postulated a benefit in relieving the system preamp from handling the full frequency range by dividing the signal after the source and using two preamps...
BTW, I also have to disagree about the wisdom of using different and possibly dissimilar amps for the different frequency ranges (subwoofer amps excluded) -- in my (albeit limited ) experience, using identical or very similar amps (and cables) top and bottom is necessary for the sound not to risk becoming discontinuous, at least with speakers that are coherent/consistent top-to-bottom to begin with.