In my opinion the LX2 and the AZ2 are not easy to compare.
The AZ2 is a very floody loght. It is onle of the SF lights with the most floody beam. Only the P60L, KX4(D), Z2-S and A2L are comparable with this beam. The A2L (with white sec. LED) and AZ2 are the two lights that can be compared 1:1. The difference between this lights is the used primary LED. The A2L has a SSC P4 and the AZ2 a K2 TFFC. The advantage of the AZ2 is that if you use low only the 4 small LED are on, not the primary LED. Therefore you have a larger illuminated area in short distances (i.e. reading a map). A LX2 would produce a bright withe point on your map.
The LX2 is a light with a lot throw and a nice side spill. But the side spill is not as bright as the spill of the AZ2 on high.
All other parts of both lights work basically the same, twisty tailcap, two stage clicky.
If you want distance you should choose the LX2, if you want to illuminate the near distance if you i.e. are walking in the forest than the AZ2 may be better. But the best choice would be getting both lights.
BTW: The 1" FM54 diffuser is great, it is the most expensive one of the diffusers, but it is made of aluminium not fiber enhaced plastics. If you have more than one 1" light this diffuser is a must have. It will fit on the Outdoorsman Series, Backup, LX2, L1, ....