I have compared the two in the same guitar.
EQ wise they are both very similar, although the tone zone feels bigger/thicker.
The tone zone is better if you just want a good all out heavy rock/metal pickup - the cleans arent great, its not very subtle, but it has a very powerful in your face relentless sound and makes amps distort very early. And despite its power, the TZ is quite warm sounding - in a kind of modern EVH sort of way.
The air zone is more versatile. Although it doesnt really sound like a JB or Custom 5, it is versatile in that kind of way - the cleans are decent (actually better than JB or C5), it can sound vintagy for a good classic rock sound because it is more reactive than the TZ to lower the gain on an amp a bit, but can also do the modern metal sound as well. I reckon the AZ has about the same output as one of the custom series SD pickups (CC, C5 or C).
In short I guess the biggest difference is simply that the tone zone is significantly more compressed, which means you sacrfice a fair bit in terms of clean/lighter distortion sounds, but the overall sound is bigger/more forceful.
Having read your last post I would say this:
If you have tried a JB, C5, CC or Custom and these arent aggressive enough for you, then go with the TZ.
But if there were aggressive enough get the AZ