The K601 and K501 are very strange beasts. They really take an unusually large amount of power to get them going, so don't be fooled by the lower impedance they have. I find beyerdynamics take a lot less wattage to run even though they are 600Ohms.
Also, I don't hear a lot of complaints about driving beyers, but they do have plenty of other SQ related issues
I would say the same about the K701 family as well in that they are picky suckers just like the K601 and K501. They are easier to drive but still a pain to get going like the K601 family.
Definitely. The K701 set have their own quarrels with amplifiers. But in my experience they don't require the same amount of power the K601 and K501 I had did.