Not all ANC are created equal. There is more than one way to implement Active Noise Cancelling
There is feed-forward ANC which is used in IEMs.
This uses a small mic on the outside of the IEM and that signal is 'inverted' in polarity and filtered in a similar way as the natural attenuation of the IEM itself.
That signal is mixed with the music signal and thus has good attenuation of outside noises and can even operate above 1kHz.
The original signal passes without changes made so switching ANC on and off should not affect tonality nor distortion but still could.
Talk-through feature is possible.
Then there is ANC in over-ear headphones which works differently.
This can be done fully analog but is also done digitally which can have slight advantages.
It works by using a microphone that is positioned right in front of the driver.
This microphone thus picks up the noises in the earcup
+ the music that is being played.
(Below AKG N60NC)
As the microphone picks up both signals, the wanted and not wanted, the ANC circuit is also fed the music signal.
Based on this input (mic that detects all) and the music one can simply 'null' these signals (by subtraction, i.e. phase reversal at the correct level for the 'correction' signal) and thus the speaker inside emits the 'contra sound' for what is coming from the outside (unwanted noises) AND also corrects the frequency response at the same time thereby improving (flattening) bass response which is often wonky in closed designs. (QC35-II
ANC on,
ANC off)
A downside is that, because of the mic-driver distance and speed of sound, the correction is limited to to frequencies below 1kHz (or so). Attenuation of higher frequencies is done purely passively.
Some headphones also add a 'target' curve (EQ) so they can shape the sound as well. below WH-1000X mk3
(
N.C. on,
N.C. off) and the
passive mode)
Distortion also could be improved by ANC
QC35-II without ANC:
QC35-II with ANC:
But alas this isn't always the case. There are also ANC headphones that increase distortion levels when switched on.
Some ANC headphones have inverse (flipped) polarity, some do not. It highly depends on the circuits used.
Below the PXC550-II in passive mode (polarity inverted)
PXC550-II with ANC on (correct polarity)
Then there are newer ANC versions that use a combination of both techniques described above and over-ears that use the IEM tech. The latter does not correct for driver distortions so the 'sound signature' does not change when switching it on and off.
These do work a bit higher than 1kHz.
The biggest upside is that one can easily make it have 'talk thru' by simply using the outside microphone as a source and mute or attenuate the music signal (if present) but of course ANC does not work. The 'mic' signal can be shaped (limited frequency response) as well.
Not all ANC is created equal as the microphone circuits have (add) noise which in some headphones becomes audible when no music is playing. The noise 'spectrum' (tone) can vary as well between models from higher pitched noise to lower pitched noise.
Downsides:
Requires (charged) batteries
background hiss (low level) may be audible without music playing.
Often the digital ones are limited in FR to 20kHz or 22kHz and have extremely poor anti-alias filtering. (PXC550-II)
and Beats:
Something to consider when playing 'hi-res' music on such a phone when using them wired.
Not all of the digital ones are limited to 22kHz or so.
upsides:
The feedback types are less seal dependent (up to a point)
NC off
NC on (same seal breaking):
No amplifier needed.
Bluetooth is easily integrated.
OE's often also have distortion lowered and better frequency response (tone) at the expense of light background noise. The better ones have inaudible or barely audible noise.