I don't own the HD-580 anymore, so I'll give you a few comparisons to the HD-600 based on what MY ears heard with it's stock cable.
With the stock cables the HD-600 often sounds more clear, yet it's more forgiving of source quality. Does this makes sense? Probably not.
I guess the HD-598 is a little more grainy than the HD-600, but the difference is under 5% IMO and requires specific music to tell the difference. Usually stuff with a large soundstage.
I compared them side by side at the same time. I even had the HD-650 at the same time also. The HD-650 is less grainy than that of the HD-600.
The HD-600 and HD-650 are not super clear sounding headphones IMO. The HD-600 is kind of muffled sounding, but the new version less so. I tried them on 3 amps and my Asgard.
The HD-600 and HD-650 are not even remotely detail monsters. If you have a lot of lower quality files, they'll be quite forgiving of them if needed. They're more revealing with upgraded cables though.
With an HD-598 upgraded cable (totally rewired cheap Mogami) the sound clarity was pushed a bit past the HD-600 and had more detail IMO.
The HD-600 with stock cable had less treble and felt at times a little more laid back, despite the extra bass. For my preferences, the HD-600 is kind of boring.
The HD-598 has a much larger soundstage (no comparison) than the HD-600, but it may be better overall on the HD-600. I didn't compare them.
To me, the HD-598 has much more detail than the HD-600 and HD-650 with an upgraded cable. Think I'm crazy? Try it for yourself!
Of course as they say, the HD-650 is technically better.
HD-598 also has much more forward sounding mids than the HD-600 and HD-650. Some may not like this. They're not that forward, but it's really nice for some music.
HD-600 also has much more bass. I hate the bass on the HD-650 and often bleeds into the mids with some amps. Barely. I didn't realize this at first.
After comparing all 3 headphones I sold the 650, skipped giving the HD-600 a 3rd try and kept the HD-598.
Basically it depends on what sound signature you like most and the type of music you like.
People who generally don't like Sennheiser headphones should give the HD-598 a try. It's definitely one of my favorites.