IMO it's completely dependent on the design and quality of the individual speakers in question.
If executed well, the active speakers advantage over passive is that the amps can be custom tailored to the drivers, and many times these active units are bi-amped with very good results. This advantage can be quite large, as I learned in listening to the passive version of my old Paradigms compared to my active version. I listened with several different amps, and the actives won out every time, by a fair margin.
That being said, a poorly executed active speaker not only won't perform as well, but you have no chance at bettering them via rolling amps.
I think the terminology for that sickness is DIYer.