I thought the HD660S were, from the Amazon descriptive text:
"The HD 660 S employs newly designed transducers featuring extremely lightweight aluminum voice coils coupled to diaphragms precision crafted from stainless steel fabric."
Not, certainly, the difference between silk and metallic dome tweeters, but perhaps not entirely dissimilar in all respects.
But yes, having different headphones, and amps, does allow different views into the same musical universe. Good, clean fun.
HD800S and LCD-3f are, historically at least, TOTL and very much reference class devices in their own continua. So, for that matter are the HD600/650, so we keep talking about them, even now.
I just shared the DT177x with my partner, a devotee of DT1990, and she was amazed and enthralled, tracks from Ott and Shpongle. She hated my Audeze.
Just looking at the membranes and it's obvious it's some sort of plastic. With the HD 660 S I think it's referring to the rear of the driver capsule and the venting system where there appears to be a metal mesh instead of the paper on the HD 600/650, seems to have the same multi-layer membrane as the HD 600/650. The membranes look almost exactly like the HD 600/650 ones, mostly clear but slightly opaque. The DT 1770/1990/Amiron Home have a big magnet with a large hole, with blue plastic capsule and paper venting around the driver, plus also a dampening cap on the rear of the driver with a rubber wahser to connect the rear of the driver to the housing. The T1 uses essentially the same magnet but machined aluminum capsule instead of blue plastic and the membrane is attached to the aluminum and some sort of fabric mesh covering and surrounding the front of driver instead of paper. The tesla's use a triple layer membrane if I recall right.
Not saying they are completely different but they do have some inherent traits due to the material.
I have heard the HD 800 S and the LCD-3(non fazor), but never long enough to get any solid impressions.
I hope to get the chance to hear the DT 177X sometime soon, but I recently got the T1.2 Black so no headphone purchases anytime soon for me.