I think the "hearing things in songs" factor is more a matter of how the headphone's tonal balance emphasizes or de-emphasizes various things in a mix. Even shit headphones can be EQ'd to emphasize the same things, assuming they can reproduce the relevant frequencies without serious distortion.

"detail" to me (and these kinds of subjective terms lack any concrete definition outside how each individual interprets them) means lack of "crud" for lack of a better word, like reverberations, resonances, "grain", etc. Stuff that doesn't lend itself to easy EQing.