Mercenary Pilot - the noise is reduced in the same way that waves in a pond are cancelled out. If its quieter with ANR, its really quieter and does indeed save your hearing. The £220 I spent on ANR headsets in my previous aircraft (turboprop) were an absolute wonder.
Rainboe - If you can, wear them on both ears. Some people argue that they want to "hear their aircraft" for things like engine failures and tyre bursts etc. I have found that I can hear a lot more from the aircraft (albeit quieter) with ANR. I do accept that the sound environment is different though. I have no idea what you fly and if its practical to use both ears on, but there are some guys at work who insist on 1 ear off for no real reason. A number of times in the three aircraft I have flown I have heard noises that have meant something with both ears on, where the Captain has totally missed it even when it was pointed out.