Active versus Passive is a complex question, only because speakers are complex. Since the speaker is at the end of the chain, the system can never be exempt from its inherent complexity.
With that in mind...
It takes great skill and knowledge to understand and apply filtering to speakers. But that's okay, that doesn't mean it's out of your grasp, it just means that you won't find the ultimate solution under your couch cushion...rather, between the pages of electronics manuals and physics texts. Get the knowledge. It's out there. It takes time to understand, but you will eventually understand it. I promise.
Just remember this - a driver's frequency response is EVERYWHERE but flat. Its resistance changes as a function of frequency, which changes the filtering response with it. Without measuring what comes out of your speaker with a microphone and a means to adjust the curves on an active crossover, you will be doomed to uncertainty. And I mean DOOMED.
So the conclusion is, if you have well-designed speakers with passive crossovers, you are fine. The passive crossovers are designed to compensate for the driver's ever-changing and renegade reactance and phase shifting. You'll lose a little power, but not enough to be alarmed about it. If you go active, then you had better be able to tell me the difference between an octave and a decade and how they roll off, and you had better be able to explain cutoff and phase shift...to start.
If you have muscle speakers and you want to make a wall of sound - have at it active. When it's loud, you can't go wrong. Garage Pro Audio is generally happy with a good day's work if they don't get feedback. Otherwise, for the audiophile, a more refined and knowledgeable approach is necessary.
So bi-amping does complicate things, but not because the amps are complex (really, they're not) but because the speakers are...and other things...
It's easy to believe that two amps are twice the power of one, and four twice the power of two, but there are other things to consider. What about the power delivery at your outlet? You'd be amazed how much power you lose in your house wiring with four amps connected to one circuit...I mean jaw dropping amazement. And what about those crossover points and what all those frequency bands you created are doing to your amplifier performance? For the most part, not much, but let me just say that one should take more care with the volume knob bi-amping than without. Yes you have more power, but it's limited power, and class A/B amplifiers heat up quicker under low dynamic range. Different drivers consume different values of power to produce equivalent sound levels, so sometimes, bi-amping is just overkill.
It really depends on the speaker more than anything I think. Know your speakers. Do you really think it matters on some cabinets that the mid and tweeter be driven by their own amplifier? A great majority, probably not. Tweeters hardly take up more than 30 Watts on the hardest of drunken kranking. Bass drivers are different. The more dedicated power the better. 2000 Watts of headroom or better for those.
I hope that helps.