Passive type speakers are a great companion to the powered mixer setup. Plug in each speaker with one cable to the powered mixer speaker outputs and you are done. Great for simple setups in all small venues like coffee houses, record stores, and small bars. Only thing that limits this setup is the power output of the powered mixer. You need to match the speakers with available power amp output. Most powered mixer have two power amp channels and work nicely with most passive speakers.
Active type speakers have the advantage of onboard amplification and processing that is perfectly matched for the individual speaker. Also great for small setups with or without a separate mixer depending upon your input count required. Active speakers can be used with any regular mixer by using a standard line level cable for hookup. The active speaker requires the addition of an AC cable to supply the speaker power. Active speakers eliminate the need for a separate power amp rack and crossover setup at the gig. Most active speakers can also be daisy-chained together with a simple signal cable connection from one to another. This allows for a flexible setup that can added onto easily.
Many speaker manufacturers have both passive and active and speakers available for just about any kind of use. A current photo gallery on the Prosoundweb.com web site showcases numerous passive and active 2-way loudspeakers available on the market.
Click on the link to view the gallery: http://www.prosoundweb.com/photos/category/C165