In my review, I said that the Bose provide the quietest ride. However, I am not completely convinced that this is the same as the best protection. ANR still makes sound to offset sound. I'm still not completely convinced that it isn't an illusion of quiet as opposed to actually quiet. The passive protection on those ANR sets is pretty minimal as anyone will notice with the ANR off. This is definite protection. However, I'm not convinced that the ANR actually eliminates the noise as opposed to making it invisible/inaudible. So it is possible the sound/pressure is there but you don't detect it. This may be enough not to get a headache from listening to too much noise all day. However, if the ear is sensitive to pressure, that pressure may still be on the ear even though it goes undetected. Kind of like RF being invisible/undetectable to us but still radiation bombarding the body. That's my way of thinking about it.
On the other hand, double bagging headsets will just as much block the audible sound as it will block the pressure. I haven't tried, but I've heard from others that the result is quieter than ANR in any case.
The choices are to put the audio inside and additional protection on the outside or put the audio outside and additional protection inside. Normally I'd recommend the Halo alone. But, when it comes to doubling up, if the sound output of the headphones is enough to reach you well through ear plugs, I still think this is slightly better than a Halo under ear muffs. The reason is cause you'd have to stick the audio tubes under the ear muffs and that will make some leakage. Whereas passive headset over ear plugs (without glasses) will have no leak.
By the way, if you do regularly wear glasses, using an in the ear headset like Halo may help compared to ANR because glasses tend to make some sound leak by.