Hi,
My two cents: After comparing the LCD-3, HE1K, HD-800 and SR-009, I decided to get the HE1K. I honestly think they are overall better than the others. The LCD-3 and the HD-800 just couldn't create the level of detail that the HE1K and the Stax can. They are still great headphones, but in the end, they are in a different (but still very awesome) league.
The hard decision was between the Stax and the HE1k. In the end (and this might be just me, as I didn't actually get a chance to do a side by side comparison), the HE1k seemed to handle bass a little better, with a bit more punch than the Stax. The HE1k also win on the image department, while the Stax seem to be able to handle some finer details better than the Hifiman.
In the end, I feel like the HE1k is a better all-around headphone: throw whatever music you want at them, and they will make it sound awesome. The Stax, on the other hand, seem to offer different levels of awesomeness depending on the track you are playing.
Answering my own question from a few days ago: IMO you can drive the HE1K with an AK240 with a decent sound volume. I've been doing it for the past 2 days and, for me, anything between 65-70 (the AK240 goes up to 75) is adequate, and you still get a little extra margin on top. It will probably not be enough for some lower volume recordings, or if you plan on blasting your brains out, but it will still allow you to enjoy most of your music catalogue.
The HE1k I tested and bought were brand new, so I will burn them in and report back