it depends on what are you looking for... I have an SRH750dj and Ultrasone HFI680 (not the 580), the SRH750 will sound better as an all rounder headphone compared to HFI580, for a bassheavy headphone the srh750dj has an overall balanced sound and tight bass, at a slight listening session this Shure doesnt sound at all like a bassheavy cans, the HFI580 would deliver much more punch imo.
the mids, I dont really know about the 580, but judging by the performance of its bigger brother (680), Im guessing that the 580 would have a more transparent mids and clearer.. whereas the 750dj has well emphasized and forward sweet mids, female vocal sounds really intimate on this pair of cans. the ultrasone would have a more drawn back mids but nonetheless still sweet but not as intimate. but then again I'm only judgung by my experience on the 680 which is quite a different headphone to the 580 although they might share the similar soundsig.
the highs, ultrasone headphones known for its glaring highs, the srh750dj also have a pretty harsh treble, but I'd say that the ultrasone might have a better extension overall...
FYI, DJ1 is the HFI500, not the HFI580..