Speakers are a reactive load meaning a combination of resistance, capacitance and inductance. Amplifiers don't like reactance. They want just resistance, alas. The less reactive the load the more the amp acts like its specs. An amplifier only needs to drive the reactance of the voice coil in an active speaker, a much easier load than a passive crossover with capacitors, resistors and inductors. Which load will the amps be happier with. It's obvious. Add in each amp doesn't have to drive the full audio bandwidth and a few other advantages, all things being equal it's no contest. An active speaker properly done is superior. The biggest problem is audiophiles think they can choose a passive speaker and amp combo better than a good designer can do a speaker combo. So active speakers are a hard sell.
Active Speakers Better? No, per Michael Borresen
The best sounding speaker I have had the pleasure to hear is made by Borresen.
I recently spent time with Michael Borresen in Seattle at a show. It was slow so
I was able to speak with him for a time. I asked him if he plans an active speaker.
His answer was a definitive and immediate "No". He said separates sound better.
His statement flies in the face of what passes in most audio corners as commonly recognized facts.
Sadly I am too technically challenged to convey any of his further explanation.
I invite all intelligent commentary on this question. Theoretical or not.