Fuel Air Explosives are Thermobaric weapons. They use atmospheric Oxygen as opposed to an onboard, carried oxidizer.
Wrong.
Conventional munitions cause damage by the heat, pressure, and fragmentation caused by the detonation of explosive.
FAE causes damage from the heat and pressure of the initial eplosion.
Thermobaric weapons cause destruction from overpressure. They do not use fuel like FAE (the exact composition is classified but is probably more about how conventional explosives are used that what).
They are effective against enclosed spaces such as caves and bunkers and depending on how they are employed (i.e. such as 200lb rocket travlelling at mach something or other [force = mass x acceleration] will penetrate armor to a certain extent but a grenade will not) can be used against armor.
Theromobarics (heat pressure):
NBC overpressure will not prevent them from causing damage.
They are not nuclear style weapons that devastate large areas.
They are highly effective in MOUT due to their ability to cause great damage in confined areas without significant collateral damage.
FAE:
FAE weapons would cause widespread damage but would have to be large enough to spread a decent amount of atomized explosive.
Their delivery is fairly complex and frankly terrorists can cause just as much damage with off the shelf items they already have at their disposal.
Trust me on that one.