While I'm no where near an expert, I've spent enough time to get some ideas on how the things are. Of course, there is a certain level of generalization I've done to make the points, but in overall, I think, it make sense.
Those who are new to this hobby if you think about where you fit within those two, you'll have much easier time to understand your own preference.
There seems to be 2 main characteristics kind of crossing each other.
1. Warm (HD650) vs Clear trebled detail retrieving (K701)
It's the common theme in speaker world as well. Some people loves warm sound with heavier bass and low mids, whereas others like clear trebled sound.
2. Lively (Grados and Denons) vs Laid Back (HD 650 and LCD-2)
One person's exciting headphone can be easier other persons ear piercing experience. The same goes to one's relaxing sound equals to others' boring sound.
As an example, I fall into warmer and lively sound side, hence Denon D7000 serves me very well.