To make things simple: AE's are in a class by themselves, just like the AXMC. No inter-compatibility with any other model. You can however mount AT/AW/AX barrels in an AE from what I've heard.
AT: Short Action, 308 bolt face, bonded AT style chassis, standard AT/AX/AW barrels
AX 308: Short Action, 308 bolt face (same as AT), bonded AX style chassis, standard AT/AX/AW barrels
AXMC: Long Action, 308 or magnum bolt faces, bonded AX style chassis, barrels have larger tenon, not compatible with AT/AX/AW barrels