Usually for those genres people want strong bass to feel the beat (what kind of bass depends on the sub-genre and their preferences) and a large soundstage. Treble is usually the next focus, though some people prefer more mids next. Having a fast response can also be important, particularly in busier genres. Clarity and instrument separation are important, but that is not unique to this sort of music. What kind of power requirements you require (mainly by whether you're driving them from a computer, iPod, etc., which will help dictate whether you need an external amp or not), how important comfort is to you, do you need isolation from external noises or to prevent sound leakage, what price are they, etc. Visual appeal is also a consideration for some people.
In that sense, the HFI-580 is certainly a very strong consideration, as it fulfills virtually all of the requirements most people have the the genre (comfort being perhaps its weakest point, and then slight mid recession).
Edited by LithoJazoSphere - 1/17/12 at 7:56am