While Chip at Grand Tire in Moab is a great resource, I'll save you the call. My good friend Jeff Edwards is Chip's Assist. Manager who also pits for BFG at Baja 1000, RCCA, UROC, and other BFG sponsored offroad events.
Here's what I recall him sharing with me when the Moab Edition tires came out a few years back.
They were made of a softer rubber compound, with rubber layers of varying durometers, as some have mentioned. This provided better grip on the rocks but the downside was accelerated treadwear, especially when installed on a heavy 4x4 that turned a lot of road miles. In light rig like an XJ, you'd still get decent mileage.
If you have a trail only machine, they were a great tire, but most folks want a tire that gives them the best of both worlds. The Moab Edition BFG's were only available for a few years. You may still find a new set out there, but they'd be rare.
Some of the Moab Edition tire technology has migrated to the new KM and KO tires, with improved sidewall construction, layered rubber compounds to give added traction and treadwear, etc.
I'm sure there's more that I've forgotten, but that's the nutshell version.