I was in the very same camp two years ago, lol.
My preferences, however, shifted 180 degrees.
I loved hip-hop and rap, with some modern electronic music and I also started with V shaped, bass heavy cans, like the Pro900s...
Now I hate the very same genres I loved, because I realized there is so, so, SO much detail masking because of excessively pumped [one notey] bass, it made me resent it.
I guess you could say I just hate the exaggerated bass then, I actually don't mind them that much with neutral gear, where there's little masking because the bass is tight [it made me realize that even those genres have some other subtle details beyond their bassy nature... crazy!].
I also actually really dig pop & rock, because they usually have just the right amount of bass to blend in with the rest of the frequencies. I obviously love many genres and only dislike very few.
As of late, treble is the area that troubles me more... The modern recordings are sometimes mastered just too brightly and are too hot up top :/ I love the music I hear, but hate the treble sometimes.
HE-560, being a very even sounding headphone, should be ideal. I feel that both my current favorite headphones [K612 & MA900] struggle in the treble a bit too, The Ks being a bit nasal and strident sometimes and the MAs just roll off waaay too quickly to provide an appreciable amount of treble extension... IMO of course.
I think I am getting picky with headphones