I have used both pickups in the same guitar.
The AZ has got a little less output and sounds a little less compressed, but only a little. It probably compares with the SD CC and C5 in output terms, if you are familiar with them. It is less bright than the JB.
While both pickups are mid-heavy, the Air Zones mids are concentrated in the lower end, giving the sound more body, and the JBs mids are concentrated in the higher end, making it slightly harsh (to my ears!).
If you are looking for something much lower in output then the AZ isnt your answer, but it is less bright and has more low end/ body if that is what you are after.
An alternative if you want less output is the Air Norton. This still has a good amount of fairly tight bass, is probably a little more responsive, it is not nearly as compressed sounding (doesnt distort as easily) as the JB and AZ, but it is brighter than the AZ.