I will start with the material differences. Trex is a brand of composite of reclaimed and recycled wood (like sawdust and pallets) and plastic (like grocery bags) fibers. Azek is a brand of 100% man made material of cellular polyvinyl chloride (PVC). We have not used Azek decking as of yet but have used substantial amounts of Azek boards for exterior trims.
We have installed quite a bit of the Trex and similar materials. One thing to note is Trex and composites are VERY hot in the sun. So if it is around a pool or you are planning to be barefoot on the decking, then the composites would not be my first choice. Azek does claim that this is not an issue with their product. Wood does not get nearly as hot in the direct sun.
Most composites and man made materials are lower in maintenance than wood decks, usually requiring only a cleaning. Wood requires stains or sealers etc. Now, keep in mind that the structure under all of these choices WILL be wood. So the life of your deck is still dependent on a treated wood sub structure.
Without seeing the application, I will not offer a recommendation as to which product is better for your project. I believe that composites are good products, but if you are looking for a wood deck that “looks and feels” like a wood deck I would go with cedar decking over a treated lumber frame.
Treated lumber for decking is not attractive, does not stain well, and the treated wood shrinks and cracks substantially in the months after installation. As for cost – from cheapest to most expensive – it goes like this: treated lumber, cedar, composites and man-made, and then exotics like Ipe’ under the names of Diamond Decking or Pau-lope’, also Tiger decking.