There seems to be a misunderstanding of how noise cancelling headphone work and what they actually cancel. No active NC headphones, no matter how much money you spend, will cancel dynamic sounds such as speech. So they are never going to block out a conversation.
Active noise cancellation/reduction is only affective in reducing constant sounds in the lower frequency spectrum. So on aircraft, that is the constant sound of the cabin air conditioning and some engine noise. Most of the noise in the cabin of modern airliners is from the air conditioning.
But they will not be affective to block out the screaming baby next to you, a chatty seat mate, or the FA coming to take your drink order. Any reduction of those sounds is purely from the isolation affect of wearing the headphones over your ears.
In-ear sound isolating earphones (such as the Shure and Etymotic earphones, not ear buds that you get with most I-Pod or MP3 players) work by sealing the ear canal in the same way as ear plug work. If you get a seal between the earphone and your ear canal, you can experience full-frequency noise reduction in the order of 20-30dB. Wearing these will affect your ability to hear and participate in a conversation.
Without reading the NYT article mentioned previously, I can only assume they were comparing so call in-ear noise cancelling earphones like the Sony NC11/NC12 with over-the-ear headphones. Any true comparison of in-ear sound isolating earphones (such as Shure E3, E4, E5) with Active NC headphones will show the in-ears to be significantly more affective at full-frequency and dynamic sound isolation.