[jamesbrownjr]

The "headphone quality" is usually resulting from the fact that there is no crosstalk. When listening to speakers in a somewhat reverberant room, the signal from both speakers reach both ears, directly and via room reflections. This substantially adds to the impression of the mix and usually mixes actively make use of these effects. (That's also why "mixed for headphones" is a real thing.)

[pdkl95]

Although this is an annoying effect, I'm fairly certain that isn't the problem. The Grado headphones fix the problem yet do not include a hardware crossfeed. Also, I use bs2b[1] (Bauer stereophonic-to-binaural DSP) which fixes all but the worst mixes (i.e. old music such as the Beatles with each guitar mixed pure L/R).

[1] http://bs2b.sourceforge.net/