The same has been said by other notable crossover/driver designers (and not just Gedlee) I have followed in discussions, both designs have their strengths and weaknesses but key as mentioned in a very different thread "if done correctly".
It's been my experience that the right way to do an active crossover is not to mimic the passive crossover. Damping, etc, have little or nothing to do with the issue, rather the ability to keep the driver impedance out of the filter function is important.
For instance it is possible to have a near-power-conserving active crossover, using a combination of IIR and FIR filters that sums to exactly unity. (It is possible to have such with a passive crossover, but it can not be as close to power conserving, and then you see interesting impedance reflected into the amp, which may or may not be a good thing depending on the amp.
An active system costs more, most likely, because of power amplifiers.