I had a 57/66 set pre-installed in a LTD Elite Eclipse and have had the opportunity to compare them to both the new JH "Het" set and the traditional 81/60 combo (but not as yet an 81/85 combination).
First let's start with the 66 / 60 / JH neck pickups: The 66 is quite similar to the 60, possibly a little rounder in terms of having a tiny bit more mid but it is a very nice pickup, quite sweet and I'd imagine quite versatile. The JH neck, on the other hand, is tweaked a little in the other direction - ie. less mids and more bass/treble. It's a great sounding pickup for cleans (the best of all three probably) but is too scooped for high gain rhythm applications and such is not as versatile as the 66 which is probably the most versatile of the three.
Next the bridge 57 / 81 / JH bridge pickups: This is where the 57 really pulls in a different direction to the other two bridge pickups. Whereas the JH bridge is very, very tight with virtually no low end whatsoever and the 81 is also quite tight but also quite scooped in comparison, making it possibly the most popular "metal" pickup, the 57 has plenty of mids and is harmonically very rich (sounding not too dissimilar to a Holy Diver) but this harmonic richness makes it very unforgiving of sloppy technique (rich is why I had to let it go in the end - I've spent too many years as a bass player!).
Both the 57 and 66 pickups are slightly hotter than the 81 / 60 but not as hot as the JH set. I had a set Crawlers in another Eclipse and I would say they are pretty comparable in terms of output, with the 57 / 66 combo possibly being a little hotter but nowhere near as hot as the JH set. ]
Aesthetically the 57/66 look really good in their brushed metal finish, the JH set look oddly out of place in their not-quite-black nickel finish when fitted in a guitar with standard black hardware and the 81/60 set look like lumps of dark grey plastic!
To sum up:
57/66 - Looks great, versatile but a little unforgiving of sloppy technique.
JH "Het" set - Great cleans on the neck pickup, ultra tight bridge (too tight?) and awkward black nickel finish.
81/60 - Slightly scooped bridge (good for most types of metal), OK neck (a bit of a compromise between good cleans and useable high-gain rhythm), grey plastic covers.
I hope this comparison helps a little - it's not that any of them are better or worse than any other (with the possible exception of the JH bridge which was surprisingly lightweight), it's more a case of finding the best one for your particular needs and playing style.