SPL refers to the sound pressure level you experience as a listener--in other words, how loud is the noise coming out of the subwoofer? Measured in decibels, the SPL is affected by the decibel rating of the system speakers, wattage of the amplifier, speaker placement and position, and number of speakers in the stereo or home theater system. SPL is a quantifiable measurement; you can buy an SPL meter at specialty electronics stores if you want to measure your subwoofer's output.
If you're after a high-SPL subwoofer, look for one whose drivers have a high power rating and high volume displacement.
SQ refers to the sound quality of the noise produced by the subwoofer. There is no hard-and-fast way to measure SQ; this largely depends on the listener's preference.
The way we perceive sound quality can be affected by a number of things, including the subwoofer's placement in a car or a room, the shape of the room and absorbing materials placed near the subwoofer (fabric, carpet, curtains, etc). At its most basic level, a good subwoofer should reproduce the desired frequency range at plus or minus 3 decibels.
Individual rooms can have an effect of plus or minus 15 decibels. As a result, sound quality can be influenced as much by subwoofer location as by the human ear's perception of sound.
Powered vs. Passive Subwoofers
A subwoofer's job is to reproduce low-frequency noise (from approximately 20 to 100 Herz) that a sound system's main speaker can't reproduce well enough on its own. Thumping bass beats, rolling thunder and booming explosions are noises that fall into this frequency level.
Subwoofers can be powered or passive--the latter uses a home theater or car stereo system's receiver to power the woofer, while the former has its own power source. Powered subwoofers, not surprisingly, let you fine-tune your sound, allowing for SPL adjustment and the filtering out of higher frequency sounds for better bass sound quality.
Overall, whether you want high SPL or high SQ, a powered subwoofer gives you more options.
Subwoofers with a very high SPL usually have a narrow frequency band--20 to 40 Herz, for example. They reproduce a small number of notes accurately, and anything that falls outside that frequency is likely to be distorted.
On the other hand, subwoofers that produce better SQ usually have a wider frequency range (25 to 200, for example) and are able to reproduce higher frequency notes accurately.
Exposure to noises over 85 decibels can damage your hearing. The cumulative effect of multiple exposures to loud noise is damage to the ear's hair cells, causing hearing loss that may start out as temporary and become permanent.
The louder the noise, the less time you can afford to be exposed to it without risking permanent hearing loss. Many home theater systems operate between 85 and 107 decibels; when in doubt as to whether yours is too loud, turn the volume down.