On the whole, though, there absolutely is a sort of "audiophile" who spends thousands and thousands of perfectly good dollars on completely ridiculous paraphernalia, because a combination of placebo effect and escalating commitment convinces him that it makes his music sound better. I don't have time to dig up a complete selection of background for you, but here's a good place to start, with a fair selection of jumping-off points for further study:
http://goodmath.scientopia.org/2011/12/30/audiophiles-and-th...
The major difference between the fellow described in this article, and the more usual sort of placebo audiophile, is that this fellow happened actually to be an electrical engineer, and thus capable of demonstrating to himself that he was full of it. Unfortunately, such acumen seems to be rather rare.
The rest are simply concerned with scientific measurement of the system. Does it produce a reasonably flat sound in frequency and phase that remains undistorted at volumes at which they listen to music.
The latter camp will highly rate headphones (or any other piece of audio equipment) that can produce a the full bandwidth of human hearing while keeping distortion low over a useful range of amplitude.
Comfort, cost, and construction quality would also be considered in the ranking.