Pros: Aggressive sound, great midrange detail, deep and controlled bass
Cons: Zingy treble, exaggerated sibilance, lengthy burn in time
Overall sound: Forward with aggressive treble, neutral to slightly cold midrange tonality and a sub bass boost.
Bass: The 680's have specifically emphasized sub bass, unlike the SRH840 and ATH-M50 which emphasize both midbass and sub bass. This is good and bad in a few ways - for one it doesn't flavor the midrange and allows the driver to respond faster since it doesn't have as much bass to choke over, but it's a less natural sound, and it loses a bit of texture.
Overall though I really like it, as it has nice sub bass performance for hip hip and electronic but stays out of the way for rock, metal and jazz, where bass just gets in the way. It does make drums a little thunderous, and if you have a really fast double kick drum it can linger too much, but overall I think it's more controlled than either the SRH840 and M50.
Quantity is about on par with the 840, with the 840 having much more midbass and the 680 having more sub bass. The extension on the HFI-680 is superior though, and overall it's great sounding bass.
Midrange: Unlike the 840 and M50 it isn't colored by midbass, giving these a slightly cold and sharp sound. Overall detail and texture is a step above as well, and it really gives guitars, strings and brass the sharp edge they need. However the midrange isn't quite as smooth or controlled as the SRH840, and while the sibilance here isn't painful it's definitely overpronounced a little. The midrange overall leaves me a little flat though - I'd like the midrange to have more presence, and vocals can come out a little cold.
Treble: The weak point on these things. Extension is actually very nice and a step above the 840, but it has a sizzle to it and isn't quite as natural sounding or controlled. It also suffered from a somewhat ragged attack that creeps into the upper midrange at times, and is most apparent on things like snare drum hits and cymbal crashes.
The boosted treble does give it a sense of aggression and energy that I really like though, and it's not as harsh as a Grado SR80i. But if you're looking for maximum fidelity there are better choices.
Soundstage: This was what I was most interested to hear when I first bought these things, and while it's certainly not amazing or holographic it is a nice effect. Seems like you're listening in widescreen nearly, as it presents you with a not very tall but very wide and unbroken wall of sound in front of your head. This gives a very good arena feel, and is more like the presentation of floor speakers, but on the downside there's little depth too it and it makes it harder to pick out individual sounds. For a closed can it's very spacious sounding though, and there's no closed can reverb.
Comfort and isolation: These are lighter, roomier, stay cooler and have a better headband than the SRH840. The pads aren't nearly as plush or wide though.
Design: Barebones, but sturdy. The headband fits fairly flush to your head and shiny metal accents are pretty cool, although they look like they scratch very easily.
Overall: At the $135 price point these are worth the price, although their sound quality lags behind the SRH840, which is only slightly more expensive.
If you're looking for a fun and aggressive sound with a small bass boost and a detailed and sharp sounding midrange in a closed can this is a nice buy.
Some half assed photography:
edit: I've gotten rid of these, they've been replaced by a SR80i. These weren't quite the closed Grados I was looking for, and for a more neutral sound I prefer the SRH840s. Also bumped the audio quality down a little - to me these are fine but nothing that special.