I listen to quite a broad genre, my regular music includes blues like Norah Jones, rock music like Queen, classical music (orchestral & chamber).
But I'd be happy with your standard listening test playlist, I believe comparison using music you're more familiar with leads to better and more accurate comparison.
Sorry, I meant to get to the comparison sooner but life got in the way. Anyway, here goes.
First, it's worth noting that both my X00 (PH) and HF580 are lightly modded. The X00 has the Lawton Driver dampening (NOT the cup part of the mod) and Dekoni Hybrid pads and my HF580 has Sendy Aiva pads. Second, this was my listening setup Laptop spdif out > Modi 2 Uber > THX-789 > Headphones.
TL;DR version
Basically, the X00 is very v-shaped and the HF580 is almost the complete opposite because it's rather mid-focused. I think for what you listen to, the HF580 is a better fit, actually, because midrange is pretty prominent for all the music you listed and the X00 is recessed there.
Bass
The X00 has more bass (no surprise there) and better slam/impact and even though biocellulose bass has more texture than regular dynamic bass the planar still has more texture and detail here and can move a lot of air if it's required. So the HF580 wins on detail, the X00 beats it in all other regards where bass is concerned.
Midrange
This is where the headphones really separate. The midrange on the HF580 is quite forward but isn't mushy or overly smooth, there is lots of detail here and it has a surprising bite. I suspect this is from some extra energy in the upper midrange. The X00 on the other hand sounds cold by comparison and vocals take backseat to everything else. Electric guitars also suffer at the hands of the X00 because it has too much treble and not a enough midrange to give them satisfying body. Acoustic instruments also have less life on the X00 since they sound so much more recessed. HF80 is the winner here, no question.
Treble
The 580 has less, the X00 has more. Neither of them sound like they have way too much or way too little. The X00 sounds colder overall but I don't know if that's because of the treble timbre or the recession of the midrange leaves the treble all by itself up there with no company. If any headphone that has less treble than the X00 sounds dark to you, the 580 probably also will, too. I didn't feel like either headphone was missing important details in this region but the X00 has more of it, if that matters to you, one way or another.
Soundstange/Imaging
Since both of these aspects are subjective, I didn't give these serious weight when I was listening. Both headphones have smaller soundstages but this is more a surprise from the 580 since it's open and the X00 is closed. I also didn't hear a clear winner in imaging during my listening test, since both do a pretty good job with it.
Conclusion
If you are looking to replace your X00 with the 580, it's not a good fit but I think they would compliment each other nicely. Although, I wouldn't be surprised if you ended up using the 580 more because it's a better fit the type of music you listen to.
Anyway, I hope that helps. Let me know if you want me to expound or clarify anything that I said. Stay safe and happy listening!
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