ANR cancels sound in narrow frequency ranges, giving you the impression that it's indeed quieter. You're hearing some things better because your hearing (and ability to discriminate one sound from another) is able to pick out sounds in certain frequencies)...but don't make the mistake of believing your hearing is being protected.
What ANR does for you is enable better communication. Think of it in that term rather than hearing protection. It doesn't block noise (ever turn off your lightspeed's ANR while flying?) or provide broad spectrum protection. It cancells certain sound waves and vibrations and certain frequencies only, giving the impression that indeed it's much quieter than it really is.
I have lightspeed headsets and bose headsets; I've used them in small piston engine airplanes, turbojet and turboprop airplanes, and even what may be the loudest cockpit in the world, the re-engined PB4Y-2 (according to sound meters I carried on board as part of a test). I've also frequently used them in conjunction with earplugs for additional protection, and when using them, I don't consider them protection, only enhancers for communication.
Conversely in my flight helmet, while I was urged to have ANR installed, I declined, because I found that I can't hear what I need to hear well enough with ANR present. The helmet alread blocks enough noise that any further decline in my ability to discern higher frequencies might mean I'd miss an engine failure completely unless I happened to be looking at the instruments, and at critical times I can't afford to be looking in the cockpit at all. Being able to hear changes in the airplane around me is very important, and while the ANR may not do much to protect my hearing, it might cause me to miss some critical cues to the health and operation of the airplane.