A key thing to remember when deciding what type of bandpass box to use is subs that tend to work better in sealed alignments work better in 4th orders and port friendly boxes do better in 6th. It's a simple and easy thing to remember and will make sure you not wasting your time when designing. All these designs are trading bandwidth for effeciency so asking if something is louder than something else, especially without even saying what driver or what frequency you want to be loud is a simplistic question honestly being laughable.
Most car audio subs with a 4th order tend to peak very hard down low. You'll see alot of these designs with peaks at 20-30hz. This isn't because of the box inherently so much as the drivers they tend to use. A good 4th order can have a response of around 1.5 octaves, maybe 2 octaves worth in a car, but it won't be as loud if you do that. General rule of thumb for any bandpass is 1.5 octaves of response.
Last thing to keep in mind is I hear on here a lot, "xth order bandpasses only play a limited range, that's why I like ported".. First thing to point out, how many of you guys CAN or even DO run your subs much over 60hz. 60-30hz is only 1 octave, bandpasses can do that, no sweat. Second, how many of with your ported box tuned to 30ish hz have anything ballparking a flat response. Generally your flat from maybe 30-50, which again is smaller than an octave. The lack of bandpass response doesn't give you any hope of fighting cabin gain to achieve a flat response, a well designed bandpass with the right drivers can sometimes do that.
For example a 6th order has 2 resonant points, with a dip somewhere between them. If you careful, you can put the dip where you cabin gain helps the subs the most, and put the upper and lower dips where you need extra bass to flatten things out. Very few vehicles will be flat between 60-80 as compared to 30-50 and a bandpass can help with that, particularly a 6th order.