I have tried both and ended up with the ATH-M50x. The Bose noise canceling feature was extremely painful on my head, I felt as if magnets were vacuuming my brain; I also tried the IEM version (QC20) and I actually loved them and didn't feel that pressure, but I also returned them because was turned off at the idea of having to use the device that comes attached to the cable and if it breaks it isn't replaceable, which for $300 isn't worth it.
So did my research and ended up with ATH-M50x. It doesn't isolate sound like noise canceling but it does a good job in an acoustic way. And I don't care about noise anyway. The quality is good, bass is strong and clear, sometimes highs can be screeching but if you amp them and get a good source this shouldn't be an issue. If you need extra sub bass then definitely amp them, like for rap and techno. Even for some classical the bass is just gorgeous.
I also have Sennheiser 598 but that's a different story, and I love them more than the Audio Techs, 100 times better soundstage and quality but the Audiotechs are fun and strong for more modern music. IMO