The very basics: a [speaker] passive crossover comes AFTER the amps, operating at speaker level. The drivers are connected to the crossover not the amplifiers; active crossover /electronic crossovers come BEFORE the amps, operating typically at [balanced] line level; the drivers are individually and directly connected to a specific amp channel that is for that driver and that driver alone.
It is hard to understand how anyone could think shoving a bunch of passive electronics with lots and lots of wire into an audio chain between the amplifiers and drivers could be a step up in quality and create a better, more pristine audio chain. I wonder if passive fans realize how much wire is in an air core inductor used in a high quality passive crossover (300-500 feet or more?). We don't do any other processing after amplifiers, why is the passive crossover somehow an exception?
There is so much science here that is quite established and well accepted, since the 60s-70s at least. ATC and Genelec were offering full [analog] active crossover loudspeakers to the market in the early 80s, some with internal amps, some with external amps. Both companies sold into home and pro simultaneously. Now there are many more companies offering active crossover speakers and some use DSP, some still analog.
There are plenty of options and choices as to how one can approach this active issue and adapt it to your liking, make it sound one way or another. It does require some work to understand what is happening, but its certainly not complicated. It is not more expensive or more difficult to operate.
I cannot help but observe the entire "passive crossover is better" argument appears to be a clear example of marketing not science.