There're many choices for subwoofer boxes on the market and it can get overwhelming. There's the sealed, ported, bandpass and the aperiodic box. Here are the differences from a certified professional.

First off, Speaker and Subwoofer boxes is more often than not the determining factor when it comes to what sound comes out of your speakers. Even a foam baffle around a 5" speaker will make a noticeable difference in how the sound system will perform.

Second, no one particular type of box is better than the other. Each box has their own advantages and disadvantages for each application. Keep in mind that one box for someone may not be better for another person.

• :: Infinite Baffle or Free Air ::
  Pros: Minimal work needed for mounting. Many modern vehicles are already equipped with a Factory sub like this. Uses very little to no trunk space.
  Cons: Isolating sound to just one area can be difficult in some vehicles. Inefficient power handling and sound control. In some vehicles, Installation can be as much as (if not more) than getting a box made for the speaker.
  --What is infinite baffle?--
• Infinite baffle is mounting directly to the surface of a vehicle (say the rear deck of a large sedan). Typical vehicles use infinite baffle for mounting speakers already. Smaller speakers are ok to use in this application. It is with subwoofers where sound quality is noticably degraded versus a subwoofer installed into a box.
  
• :: Sealed Boxes ::
  Pros: Sealed Boxes have great bass response and a very smooth bass line, so music will not have surprise power notes in it. They also tend to have a better low frequency handling compared to other types of boxes. Sealed boxes also allow the speaker to transition from one note to another faster and cleaner compared to other boxes. For those where space is at a premium, sealed boxes make an ideal small enclosure.
  Cons: Sealed Boxes do not have as high an efficiency for speakers requiring more power to make more sound. Simply put, they are not as loud as the other boxes for the same power. This type of box does not allow heat to escape easily, so playing long and hard risks damaging the subwoofer. Also, if there is distortion in your signal going into the speaker, it is more noticeable in the upper bass notes. For some, this may not be a con.
  
  
• :: Ported Boxes ::
  Pros: The output is better than sealed due to the port adding more boom. Essentially the port acts as another speaker and can double the amount of sound. The box also has a better low frequency response versus the sealed boxes. Tuning the box to specific frequencies gives even more boom as needed for the user. Because the port also somewhat allows the air to circulate, you can play your speakers longer and harder.
  Cons: Ported Boxes tend be harder to get just right for particular speakers. Their design also may cause distortion in your speaker. During times where one is playing long and hard, the heat may not spread out evenly. They also do not provide a cushion for the speaker and overdriving speakers can be an issue. These boxes are usually larger than sealed boxes. More often than not, they double the size needed per speaker.
  
  
• :: Bandpass ::
  Sizes vary but are usually in between sealed and ported boxes.
  Pros: Bandpass Boxes will sound louder at the tuned frequencies. It also acts as a filter for unwanted frequencies. Due to the sealed portion of the box, there is a cushion for the speakers so one cannot easily overpower a speaker. These tend to provide excellent results for sound competitions.
  Cons: Very unforgiving. Bandpass Boxes are sometimes known as Speaker Destroyers. They filter out hearing the speaker distortions, but do not prevent the speaker itself from distorting. If the distortion can be heard out of these boxes, it is most likely too late to fix the problem. They are also usually tuned to a particular speaker or range of speakers specifically.
  
  
• :: Aperiodic ::
  Pros: The rare Aperiodic Box is the ultimate box in terms of sound quality and output. It is as smooth sounding as sealed and as powerful & loud as the ported box. They do not harm the speakers in any way, allow the heat to exchange properly, and cushion the speaker so it does not distort easily. In some cases, the box can be even smaller than the sealed boxes.
  Cons: Most unforgiving until it is tuned. There is no computer program that can tell you how to make it and what are the measurements. It is also only good at the tuned air pressure. Changing from one altitude to another affects the quality of sound. As little as 1000 feet in altitude affects it. They also tend to be very pricey. Spending over $1000 per subwoofer is pretty common.