Do you have any scientific studies or something that says this?
I do not, but try using the search function I'm sure this topic has come up before.
My understanding is that an ANR headset will reduce fatigue because it cancels some of the sound electronically rather than passively meaning that the headset construction can be made more comfortable.
A passive headset works by generating a pressure seal around your ear, hence it needs to hold the ear cups firmly against your head. With ANR part of the noise is electronically cancelled by destructive interference (reproducing the sound with inverse phase) and therefore the headset does not need to clamp the ear cups on your head so firmly. The extra equipment in the headset may also reduce passive noise reduction because it takes up space that would have been used for sound proofing.
Now passive headsets stop sound before it gets to your head. ANR headsets attempt to cancel the penetrating sound inside the ear cup using the headset speaker. Arguably this is not so good for protecting your hearing as vibrations may still be getting inside your head, particularly at low frequency. The cancellation is not 100%.
One interesting point is that with a passive headset you may be damaging your hearing by turning the radio volume up too high. With an ANR headset the perceived noise level will be lower so you may use the radio at a lower volume.
I'm not an expert so if anyone knows more about this or knows that my understanding is wrong, please do say so.