I personally find the HE-560 better for my tastes than the HE-6. Comfort and aesthetics aside, the HE-560 sounds more balanced and natural compared to HE-6. You could argue that my HE-6 wasn't properly amped, that I haven't got to hear its full potential (but hey, who has really?), but I think it's a matter of sound signature preference rather than absolute terms of technicalities. For the record, I do admit that a well-driven HE-6 beats the the HE-560 in many areas. But then again, I'm a kind of guy who prefers SR-007 MK1 to SR-009 over a BHSE, so 'nuff said.
Here is how I would rate the headphones/amps I've owned or auditioned, based on my preferences. All the headphones were unmodded, in their original stock form (no Anax mod, grill mod, etc.).
0. Smyth Realiser A8: Okay, this isn't really a headphone system but rather a unique audio processor, but I think it deserves a special mention because no audio equipment, be it the best headphones or amps out there, blew me away like the Realiser did. I know some folks personally don't like the way Realiser alters sound, but for me, I can no longer imagine listening to my headphones without it. At least to my ears, even a modest sub-$1,000 setup comprised of a Sennheiser HD600 sounded so much better and more listenable than a $5000+ electrostatic setup with the Realiser in the upstream. Seriously, if you have over $4,000 to spend on your system, I strongly recommend you get the Realiser first and spend the rest on the headphone and amp rather than spending the entire money on headphone and amp. For easy-to-drive headphones, you may not even need a dedicated headphone amp; the HD600 and LCD-X sounded quite good out of Realiser's own heaphone out.
1. HD800 (via HPA-3000's hi-Z output): Absolutely the best system I've heard to date for the best audiophile recordings out there. F**kin' brilliant imaging and breathtaking soundstage, incredible frequency extension and superb mids and bass quality. There is no treble etch here, but using a Black Dragon cable makes the sound ever so slightly warm that creates an ideal balance. HPA-3000/Black Dragon/HD800 FTW all the way. I think it's a shame the HPA-3000 is not well known in the Head-Fi community yet.
2. HE-560 (via HPA-3000's lo-Z output): Very natural and balanced sounding, with a huge open soundstage and the right amount of bass oomph. My favorite planar magnetic headphone by far, and slightly preferable to the HD800 system above fore more contemporary recording which requires a less forgiving sound. Maybe not the last word in terms of sheer technicalities compared to a well-driven HD800 or HE-6, but for my tastes this is as good as it gets. For less than $1,000, I think the HE-560 is the best headphone I've purchased in terms of performance/price ratio value. Kudos to HFM for such an exceptional feat!
3. HE-6 (via Pathos Classic One MKIII's speaker outputs; so much better than HFM's own EF-6 or even RSA Dark Star): By now it is no-brainer that a powerful decent speaker amp could outperform most TOTL dedicated headphone amps when it comes to driving the HE-6. At $3,000, the Pathos Classic One MKIII should be a serious amp to consider for any HE-6 owners out there. At 70W per channel it has more than enough juice to make the HE-6 sing, but the sound quality is where it's really at. Nevertheless, it's a bit bright in some recordings, and using an OCC copper aftermarket cable didn't seem to help much.
4. SR-007 MK1 (via BHSE): Perhaps most natural and balanced sound I've heard, and technically flawless in almost every way, but leaves a lot to be desired in the bass quantity department. I'm by no means a basshead, but the bass just wasn't enough for me, and sounded rather too polite as a result. Maybe if I grow older, the SR-007 MK1 will grow on me. The best electrostatic headphone system I've heard though, and preferable to SR-009 for my tastes.
5. Sennheiser Orpheus HE-90 (via HEV-90): The biggest "wow" factor I've heard in any system, the magical sound Orpheus captivated me the moment I listened to it for the first time like love at first sight. However, even during the short period of time that I got to audition it, I realized the sound was colored and somewhat unnatural. It was a unique coloration though, and I'm sure people who like their music to sound romantic without being overly warm or lush would love this system. A collector's item, for sure.
6. HD800 (via maxed out ZDSE or Bakoon HPA-21): ZDSE and HPA-21 has a different sound signature, but both amps take the HD800 to a whole new level. Although I personally preferred the ZDSE to HPA-21 by a small margin, neither amp could take that treble etch off the HD800.
7. TH900 (via maxed out ZDSE or Bakoon HPA-21): The best closed headphone I've heard, the TH900 pairing with ZDSE was just sublime. I still miss it every now and then.
8. LCD-X (via HPA-3000's lo-Z output): I had high hopes for the LCD-X, but was left a bit disappointed by its V-shaped sound signature. The TH900 above is V-shaped too, but its recessed mids was remedied by the ZDSE's magic (which tends to have a forward-sounding, rich mids). I didn't get to try the LCD-X with another amp so maybe the HPA-3000 wasn't an ideal match for it. I personally did not like the LCD-X's treble; it is not sharper than the HD800 in absolute terms, but it stands out too much in comparison to the mids. Still, I preferred it overall to pre-Fazor LCD-3.
That being said, I'm looking forward to auditioning other TOTL amps (such as GS-X mk2, Teton, L-2, 445, or LAu) with my flagship headphones someday. I also haven't auditioned the Abyss or LCD-3F, so they are on my auditioning list too along with HFM's upcoming statement electrostatic headphone. For the time being though, I couldn't be more happy with the two headphones I own.