I own both these phones. I really like the HD600s, but there are aspects of the HE-500 sound that I also really, really like.
The 600s sound a bit too dull/veiled and lacking in bass 'quality', but they are very easy to listen to.
The 500s have a bass sound that I really love, but their treble veers from shrill to piercing to occasionally painful.
I've listened to them both through a range of headphone amps - JDS O2, Schiit Asgard mk1, Graham Slee Solo, Lake People G109S and Audio-Gd SA31SE and my feelings about how they sound are basically the same. The closest to perfection is HE-500+G109S, but the there's just too much treble.
I currently have access to the G109S and the SA31SE. Is there a 'phone out there that will give me HE-500-quality bass, but without HE-500-quality treble?
Money? £1000/$1600, but I'd be happy if I didn't have to spend quite that much. Audeze LCD-X???
Difficulty: I can't/won't buy an Emotiva mini-X A-100, and I have no interest in valve amps...