Aside: For those unfamiliar with active cancellation, this is the same technology that is used in the Bose line of headphones where an out-of-phase signal is induced under the ear cup that cancels out the sounds that leak in from outside, thereby letting you hear the audio being cabled in from the media player/device (e.g. MP3 player, radio, etc.) even in moderately noisy environments.
The design trade-off is governed by the constraints that active noise cancellation does not work very well at high frequencies but does work well at low frequencies, while passive cancellation at the low frequencies requires massive (i.e. heavy) sound absorbing materials, which would weigh the airplane down. At high frequencies, the materials can be much lighter. So, as you can see, the design trade-off works out very neatly - active at low frequencies and passive at the high frequencies.
One design detail that stood out to me is that they use 24 microphones to provide feedback to the cancellation algorithm so it can continuously adapt to the changing noise environment in the cabin. Those 24 microphones are coupled to 12 loudspeakers to produce the anti-phase cancellation signal. The numbers of microphones and loudspeakers tell me that this is a serious system that is designed to reduce noise through-out the cabin, not just in a limited area. My hat is off to them as this was a seriously challenging design problem.