I finally bought a pair of these after a long search for the best closed(isolating) cans, with need for an amp being a big price/convenience factor.
I did get a chance before buying to try a couple of pairs, and compare them directly to some akg's, other beyer's and KRK-8400 and shure 840. I was also able to compare the latter two directly to several others (without the 660's at the time).
The models to beat:
Before I got to try the DT660's my favorites were the KRK's and Shures. I love the detail, imaging, and separation on the KRKs as well as the well represented highs, but somehow they often sound a little thin and distant in the mids, and most of all they are incapable delivering loud bass, and if you try to force them to they sound very boxy/distorted with poor impact. The bass issue is hard to ignore for me. I noticed the distant mids most when comparing to something like the Shures that somehow just have a really cohesive full sound that is instantly immersive and hard not to smile about in spite of (or even related to) very poor/compressed imaging. The Shure seems to have a better impact all the way up through the lower mids and this could be related too. I just thought I couldn't be very happy with the shortcomings of either of these phones, so I was still searching, and after David's praise, went searching for the DT-660's.
Sound:
The DT-660's seemed to me to have sort of 90% of everything from both the competitors rolled into one. They aren't bass tilted but the bass quality is solid (not boxy) and stays that way for loud bass. Unlike the KRK's, they are very capable of delivering strong impactful bass and sub-bass. They just don't do it when the source, or your equalizer, doesn't ask for it. The imaging is quite impressive, certainly far better than the Shures, and they have most of that overall full, powerful upfront engagement of the Shures that somehow leave the KRK's just a bit flat footed. Probably much of this is again due to bass capability. There's certainly nothing missing in the highs either where they pull out detail impressively, very balanced sound to me. Finally, as has been said, these are great without an amp, which is probably related to the fact there is really more than plenty of volume to spare from any portable source. While I haven't tried the DT660's with an amp yet, I'm already loving the sound quality without one. That's a great simplification and big value/dollar factor.
Other closed cans:
I did also try MDR-1's and the similar sounding Momentum's, but with a strong preference for the Momentums for me. Both had a sound that was way too warm. The Momentums are great headphones with undeniable sound quality. I'd love to own a pair, but for my primary enjoyment I just can't live with losing the highs under that big fluffy warm blanket, no matter how cold it is outside. Maybe some EQ would make those perfect as well as amazing. Going lower end, I tried CAL's for a minute. Great initial sound signature, but as I see it they are toy compared to these other headphones. There could be a case for them for someone vs the KRK's. Of course I also tried other Beyer's. I had tried the DT770's (a couple of varieties) head to head with the KRK's and Shures. I was really impressed with their ability to deliver bass impact, helping me realize what the KRK's couldn't possibly do, but the bass tilt was decidedly too much for me, although far less pounding than m-50's. I also tried a few AKG's, don't remember which ones. All I remember about that was that none pulled out details, as well as the DT660's.
Break-in:
After buying a pair of DT-660's my initial reaction was that they were slightly tight sounding, boxed in, and holding back something compared to what I'd heard in the store. For the first usages I used different, probably worse, source hardware though(un-amped in all cases), so it's possible that's a cause, but I did go ahead and burn them in for 100 hours(with programmed breaks) on pink noise. I do believe that this made a real change. I don't believe in cable voodoo for a minute, but I think these headphones may really "open up" with some burn in.
Comfort:
I find the velour hotter than fake leather and this is uncomfortable if you're tying to save on the AC bill in the summer. The KRK's were without question the most comfortable, being very light and cool. The Shure's weigh more than the DT660's but felt a little lighter because the headband distributed and controlled weight a little
better(I actually like the Shure headband). My new DT660's have been better than the store demos though. The ear cups are bigger around than needed and seal well on me without fuss. The ear cups are not deep and my ears touch ever so slightly, but unlike the Shures it's not painful or fatiguing, or even noticable after a few minutes.
Isolation:
As for isolation, I think they are best of the bunch and I find them very enjoyable on airplanes. I'll just add then when even a little sound is produced, they seem to isolate better than they really do, probably because of clear imaging.
Final Thoughts:
So, I'm new to good headphones. I've compared side by side many closed phones now up to about $400 range, mostly lower though. To me they all had clear, non-subtle differences, and these seem to be the real all-around-er's. I don't mean that in terms of suiting everyone (or every genre I suppose) but in terms of doing everything really well and nothing exaggerated. With my experience I cannot dispute the claim of this thread.
See my follow-up here:
http://www.head-fi.org/t/559542/i-truly-believe-these-are-one-of-the-best-classical-music-headphones-ive-ever-heard/345#post_12326804