To test the claim, I took both headphones on a train trip. I tried them out in the quiet car because noise-canceling headphones do a good job with consistent background sounds, like the rush of wind, but do little to shut out chatty travelers or a crying baby.
The simple test is to turn the noise canceling on and off without any music playing. Headphones dealt with four distinct sounds there: a whirring ventilation fan, a low rumble, the wind rush and the clatter of the tracks.
The Bose handily dispatched the wind rush, clatter and rumble, but the fan noise became more apparent (not louder) in the absence of the other sounds. NoiseHush went two for four. It wiped out the wind and clatter, but the rumble and fan still came through.
Music also fared better on the Bose. While the NoiseHush had pleasing sound, it lacked the clarity and detail I could hear with the Bose. The Bose uses a single AAA battery and the NoiseHush uses two. The NoiseHush does have one feature the Boise does notvolume control on the headset itself.
Which is really better It comes down to how much noise reduction you need and how much you want to spend. At a third of the price, you are getting more than a third of the Boses performance from the NoiseHush.
Personally, I still prefer well-fitted, in-ear buds for travel. They are much easier to carry, and while they let in some hiss and rumble, they reduce the overall volume of all outside sound. And they even help block out smartphone-addicted seatmates.