ANR should be thought of not as protection for hearing, but as clarification in communications. ANR is more illusion than fact; while you don't hear or perceive vibrations or sounds so much in certain higher frequency ranges, assume that you're safe from hearing damage.
ANR reduces fatigue and it enhances communications. One can turn the volume down and hear. One can relax more.
ANR does mask some sounds. Depending on the aircraft and the phase of flight, ANR can mask an engine failure. In other cases, depending on the phase of flight, an engine failure can be unmistakable, even with good ANR.
ANR masks higher frequency sounds. With many ANR headsets, voice communication within the cockpit can be enhanced, because distracting sounds are eliminated or reduced, and one can still hear cockpit sounds, switch movements, voices, and low frequency vibrations.
At the moment I'm using a Bose QC-15, with a U-fly-mic. It's excellent in terms of "noise reduction," and I find I understand communications much more clearly. This is especially useful when traveling internationally, with the myriad of accents and voices one encounters on the radio.
I hear best with both ears. However, the headset is effective enough that I cock it off my left ear whenever talking to others in the cockpit, or during takeoff and landing. Enroute when there's not so much going on and little cockpit chatter, I put the earphones over both ears. This particular installation has a jack port on the bottom of the mic assembly which allows an auxiliary set of earphones, in the event there's a problem with the bose QC-15 headphone.
The entire assembly is relatively inexpensive, compact (a big plus, as I've already got enough stuff in my flight bag, the reduced space that the headphones take up is important), and handy. It's got a music input, and I can use the headphones when deadheading or riding as a commercial passenger somewhere. I can use it for the aircraft entertainment system, or use an mp3 player.
I've used Bose headsets such as the Bose X quite a bit in all kinds of aircraft, from noisy shakers like the Cessna Skymaster to the Cessna 210, to Learjets, King Air's, and Large aircraft of differing types. They work great. They're a good investment. I've tried the new A20, and it's the Bose QC-15 entertainment headset technology, turned into an aviation headset. I was on a flight right after they were released in which a crewmember was wearing a newly purchased A20. He let a check airman on board try it out, as well as the flight engineer. Upon landing, the flight engineer went to his hotel room and ordered one, as did the check airman. It was that good.
I've got several different david-clark type headsets without ANR. I don't like the hotspots that develop, especially when wearing them for long periods in hot environments. I use the Oregon Aero headband on each one, as well as the Oregon Aero temper-foam ear seals, and the hush kit by the same company, in the earcups. The hush kits are high density foam designed to supplement what's already in the headset. Combined with the ear seals, they make the headset a lot quieter. The headband is wide, with sheep's wool, and also makes the headset a lot more comfortable. In particularly loud airplanes I've used this along with earplugs quite successfully.
In the PB4Y, the noise level without hearing protection was into the pain threshold. I used ear plugs and the modified passive headsets. When ANR first came out, a cockpit crewmember bought a headset. I tried it, and was amazed at the difference that could be felt simply by turning the headset on and off.
Whether you get ANR or not is up to you. It's best if you try various headsets before you buy. What works for you doesn't necessary work for someone else, and visa versa.
This subject gets beaten to death. A little effort with the search feature will yield more information than you can use.