On the 767/747 and 380, we only use the company headsets. The 747 were noise cancelling, though I wish they all were. The 380 is reasonably quiet, but, I really preferred the silence of the 747 with headset. The reason the company eventually coughed up for noise cancelling on the 747 was that they were having substantial hearing issues with pilots who'd been there a long time.
Whilst wearing the headset isn't mandatory (from the company) once in cruise, I don't allow my crew to remove them. The reason is that having their speaker turned up, whilst I have my headset on, makes any radio calls hard to understand, and also because I prefer them to use the intercom when speaking. I've had too many years of aircraft noise, and don't need to add to that unnecessarily.