I own both the HD6XX and Auteur Classic, and I find the Auteur Classic a pretty easy win for classical music. If nothing else, the soundstage of the Auteur Classic is way wider, deeper, more holographic, and things are more evenly spaced apart. But impact is significantly better as well, the upper mids aren’t quite as shouty as the 6XX (as per my personal preference), and extension is better on both ends. Resolution is better as well, though not miles ahead.
I still keep the 6XX around because its overall signature is so pleasing for intimate vocals, and it’s still the most comfortable headphone I’ve ever worn. It has a warmer lower midrange too, and still a more natural timbre to the treble.