At ~300$ there not cheap, but not only do they help save your hearing they are also less distracting for those around you.
Noise canceling works by playing back the exact environmental frequencies through the headphones, 180 degrees out of phase. So from the perspective of your ears, noise canceling does lower the absolute volume.
If active noise canceling seems to lower conversation volume, it is because you've convinced yourself it should. No DSP located on your ear can analyze and cancel an unpredictable signal like conversation before it reaches your ear. It can be effective against drone sounds like motors, rushing air, etc. because the same cancellation signal works now as did 100ms ago. This is not true of human speech.
Opt for a pair of well-fitting in-ears. If you have the money, see an audiologist for a custom fit. With high-quality earbuds and a good seal, you can play music at a very low level and still 1) hear all its detail, and 2) not perceive outside sounds.
The noise isolation is so strong that I can't even listen to music at higher than half volume without discomfort.