If I have a pair of phones that have a ton of detail, like AKG K701s with the pads removed, the sound can be sterile and distinctly unmusical, though it may have pretty harmonies. If I have a pair of phones with flat treble and boomy bass, it will impossible to listen to no matter how good the music is.
That said, having both detail and musicality is the only only one I'd pick. Look at it from the standpoint of spending money, and see how quickly you say, "Both."