One point of confusion is that most active speakers sold today use a portion of their box inner volume for housing amplifiers. The percentage of thus used up volume may range from 10% to 50%, depending on size of the speaker, number of transducers, amp technology etc.
Thus, an active speaker of a certain external volume may acoustically behave like a passive speaker of a smaller volume.
This may translate into higher level of distortions at a given output level exhibited by an active speaker, compared to a passive speaker of the same external volume.
This may also translate into the active speaker going less deep in -3db frequency than its external volume would suggest.
Rules of thumb for traditionally proportioned speakers:
Active speakers with a woofer less than 6" tend to be unsatisfactory in many respects, despite the fact that they may sound superficially well.
Active studio monitors with 8" woofers tend to sound comparably to passive speakers with 6 1/2" woofers, on the measures of distortions and bass extension.
Active studio monitors with 10" woofers usually sound wonderful, especially if they are three-way.
Active studio monitors with 12" woofers tend to rival the best audiophile passive speakers out there.