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.
Both of the above statements apply to both active and passive noise canceling. With both types of noise cancellation, they don't stop acoustic energy that doesn't go thru the ear. So it won't stop your teeth from rattling, for example. A good passive headset will have a low perceived noise level, so you would also turn down the radio volume while wearing such a headset.
There is one significant difference between ANR and PNR[*], which is that ANR is more effective than PNR at low frequencies, while PNR is more effective than ANR at high frequencies. In the single engine piston trainers, you'll find the bulk of sound energy at low frequencies (I'm not sure about turbine engines - I haven't run into any good docs for them).
- S
[*] Well, apart from the $$$$ that you'll pay for ANR.