box as in box type? well sealed usually yeilds the best sound quality but ported will be louder... ported if done right can sound great (still usually a small step below sealed thou). um sealed will be more linear when looking at dbs in different hz (meaning if you hit 130 at 45hz you will be very close at 46 ect)
where as ported will give you a hump (meaning you may hit 135 at 45hz but only 131 at 42) especially around the tune of the box. boxes that are ported high liek 50hz ect are really spl only and sound shitty for music but yeild good numbers, something like 30 will give you alot better sq but at a loss of spl... which is why the actual tune freq is so important.
then you have bandpass boxes, these are good and bad, they will usually have the most spl for any non spl only design... but they have bad sq overall and only play a small range of freqs. they also will lower any woofers life considerablly... mainly because you cant hear distortion very well... so while you are clipping up the amp and making the woofer work harder (trying to get all that air through only ports is hard on the woofer) plus the actual tuning and construction of such a box is hard
there are also several other types of boxes but again they are hard to constuct and take alot of time/knowledge