The purpose [of comparing active and passive versions of the same speaker] is so blatantly obvious. Compare them side by side to see what the actual audible differences are. Plain and simple. Geddes has done this with his speakers. His conclusion was the difference in sound quality between the active and passive versions wasn't worth the added cost of an active version.
Earl was commissioned to build an active version of his Summas, and did so. He compared that version side-by-side with his passive version and what he told me was that there was no audible difference, and so he would never build an active version again.
As an aside, while Earl is definitely an objectivist, he may be the most intense listener I have ever met. He has a friend who is a solo piano recording artist. Earl listened to and critiqued the sonics of one of his friend's albums, and his friend was so impressed with Earl's ability to hear little problems that everyone else had missed that he said he would never put out another album without Earl listening to and critiquing it first.
Regarding passive vs active, as a speaker designer, there are things I can do actively (and especially with DSP) that I can't do passively, and that is very attractive.
Over in the studio speaker world, actives totally dominate the mixing monitor end of the spectrum. Those are the smaller speakers you see on top of consoles (or, more recently, firing over a bank of computer monitors). That sucks for me because I have an idea for a somewhat unorthodox mixing monitor whose radiation pattern would work really well for that application, but I'm not an amplifier technician and don't want to manufacture something that I can't fix.
At the other end of the spectrum, big mastering monitors, passives outnumber actives, though not by a huge margin. I spent some time on a prosound site reading threads on the active vs passive debate, as far as mastering monitors go. Here's what I came away with: There is relatively little sound quality difference between top-flight implementations of the two, but better amps are available if you go passive, unless of course you go active with separate amps, which is the most expensive route. Also, if an amp goes down in a passive system, you can throw in a substitute and keep on working; if an amp or crossover module goes down inside an active speaker, a critical part of your studio is shut down until it gets repaired, unless you have a spare active speaker on hand (which many studios do, just because the money they stand to lose if their mastering capability is down for a week or more could be crippling).
There is a third application, less well known to the outside world, that of "tracking monitor". Those are the speakers that the engineer listens to while the musicians are laying down a track on the other side of the big glass window. And then when the musicians come back into the control room and say, "dude, how'd we sound??", the engineer plays the raw take back for them over the tracking monitors. Superb accuracy isn't required, but superb dynamics are, because they want to hear the same mojo they had going on a few minutes ago. And the engineer really wants to impress his clients - the musicians - so they need to sound really good even if they aren't objectively super-accurate. Anyway, passives dominate the dedicated tracking monitor market.
Imo tracking monitors and main monitors are the applications that most closely approach high-end home audio; mixing monitors have a highly specialized task that emphasizes articulation over other things that also matter a lot in home audio. Not that this precludes actives for home audio by any means!
I was a dealer for ATC for many years, and was sorely tempted to become a Klein & Hummel dealer at one point, but the price of entry was too steep for me at the time.