Active playback systems are intrinsically better. All professional grade and most high end 'audiophile' systems are active and have been for the best part of 30 years.
However a prospective buyer needs to be aware of the difference between true actives and the common practice of putting the amplifiers(s) in the same box as the loudspeaker itself.
Active and passive are types of crossover.
In an active system the incoming signal is split into 2 or more bands before being sent to the amplifiers. There is one amplifier per speaker cone. Usually in small or mid range parts the amps are included in the same cabinet as the speakers but not always. In high powered, top of the range systems the amps and crossovers can be kept separate.
In a system with a passive crossover the incoming signal is first amplified and then sent to the speaker cones via the crossover. The amplifier is usually housed in a separate box. Not always though. A passive system with the amp in one of the speaker cabinets is called a powered system.
The advantages of active should be obvious. No power lost as heat in the crossover and an amp specifically designed and tuned for each individual cone. The disadvantage is added cost over passives.
The advantages of self powered (both active and passive) is the that they should be cheaper for the same quality due to economies of scale. Selling one product rather than two. The disadvantage is that if it is done too cheaply the proximity of the transformers for the amp and the speaker cone itself leads to higher self noise.
So if money is no object active speakers with the amps and crossover located remotely would be best. Leading brands of actives with the amps in the cabinets are also excellent in the near and mid field role.
If you are buying on an limited budget powered systems are almost always better value than separates.
The trick is what to do in the middle range. Sometimes a passive system will sound better for the same money than the equivalent active alternative if the manufacturer has cut too many corners to hit a price point.
The bottom end of the true active speaker market is defined by Mackie, Yamaha and JBL. So if you have ~$500 and up to spend then buy active monitors. If you have less than ~$250 buy powered monitors. In between it might make sense to either save up a bit longer or buy separate amp and speakers with a passive crossover.
ed: rd spl :(
Edited by RonaldDumsfeld - 6/12/14 at 4:47am