There is no difference between active and passive version of the same loudspeaker in terms of sound quality. If drivers (that is, woofer, tweeter, etc.) and cabinet design are the same, performance is the same.
If we consider the electrical reliability, an active speaker is virtually more fragile; on the other hand, a mismatch between power amp and speakers, by not taking into account power, impedance, etc., can damage both parts.
Price. Comparing two identical loudspeakers, one active and one passive, it is clear that the passive is cheaper. Price can often be 30-40% less, since there is no amplifier and/or for other commercial reasons. Of course, this saving will be spent on a power amp, a mixer and connection cables.
For a real comparison it would be better to consider the entire audio system and not simply loudspeakers.
After all, if we estimate the total amount of these two supposed systems, we will realize that the difference is minimal and much depends on quality of each component.
Nevertheless, active speaker has an advantage over passive one: with a smaller initial investment (cost of a single speaker) we can start making music immediately and complete our system later. Vice versa, in case of passive speakers our initial budget must be enough to purchase all components listed above.
After understanding the differences between passive and active speaker, pros and cons of each solution, and how they impact on price and quality, we must give an answer to a basic question: what is the best solution for us. Obviously, there is no single answer, but each of us will answer taking into account some important factors:
If your initial budget allows for a complete audio system, like those described in previous section, there is small difference between active and passive system; but with a limited budget, then an active loudspeaker is the only way to go.
If you are not familiar with concepts like RMS, program and peak power, speaker impedance, sound pressure level, etc., the easiest choice is an active speaker, that only needs a power cable and an audio cable to connect your sound source!
If you feel a little more techie and comfortable in setting up a small audio system with passive speakers, perhaps this is the best solution, also because your technical education goes probably side by side with your need of higher audio performance.
It is very important to know what kind of source you have to amplify before your purchase. If you are, for example, an acoustic guitar player, and the only way to amplify your guitar is through a microphone, you will need a loudspeaker with a Cannon input (balanced XLR); if you have an electronic piano or a DJ console, you will need a 6.3mm Jack phone input or RCA cinch, and so on.
In all these cases, an active loudspeaker can be OK for your needs. Many active loudspeakers include all this kind of inputs, but it’s important to make sure of that when you choose the speaker.
In order to know if one or two active speakers are enough, or if a mixer is required, you must take into account how many musical instruments, microphones and other sound sources must be amplified. Very often, active speakers have a small built-in mixer (3 or 4 channels) that allows you to use, for instance, a microphone, a CD player, an acoustic guitar, and route the mix to a second speaker. If this is your need, the active speaker is OK; otherwise you will have to buy a mixer, and in this case, the differences between the two systems become minimal.