I had AKG headphones. I noticed a difference when noise cancellation was on, but there was a weird humming sound and they didn't work very well for me. Also, they're very bulky and you can't wear them while sleeping.

> With white noise and earplugs as well, I literally can't hear a baby screaming.

That's one benefit of headphones: if the earplugs aren't enough, you can do earplugs + headphones for ultimate noise-cancellation.