Thought I would report in, keep this thread going...
I've lived with the HE-4 for a couple months now, as well as my Denon AH-D5000. Both are stock except for new cables (balanced to attach to my Schiit Mjolnir/Gungnir combo).
I got the HE-4 and then added the Denon. I thought the Denon might be my final headphone as I thought I wanted something more in-your-face. Granted the HE-4 has plenty of weight to it (sound-wise) but I have yet to make up my mind. I will switch to one or the other and decide "wow, this is awesome, this is the ONE). And then switch to the other a day or two later and think the same thing. I listen primarily at work in a closed office, so I listen for long stretches and relatively undisturbed from outside noise. Both work well for my environment.
I find the Denon to be better for CD recorded music, the detail is a notch higher, the highs and lows are strong. I read the reviews that stated the Denon had too much bass, and I scoffed at it. But after listening to a lot (my fave genres are rock, jam bands, pop electronic, etc) I am starting to see how people can say that. The bass hits hard and it can be overwhelming at times. But it sounds so precise and in your face, its hard to find a fault. It gets you in the mood, for sure. With some of my Widespread Panic rips it is absolutely brutal with the bass.
The Hifiman goes on and I am struck by the tone. It has treble, it has bass, but its focus is on the tone; the midrange grips you and tantalizes. I find I like it better for my vinyl rips (I'm fairly anal about vinyl ripping)... some of my Grateful Dead, live shows sound expansive and while they feel less dynamic, they put you there in the crowd a lot easier. If I had to choose, I would probably end up with the HE-4 (which is why I'm posting this here). The HE-4 are not easier to balanced on the head, as they are cumbersome, but with the Beyerdynamic velour pads, they are comfy on the ears. I have no problems wearing them all day at work. The HE-4 are also open-backed so don't cause my ears to get warm (though to be fair, the Denon's aren't that claustrophobic in that regard).
So if I was to choose an upgrade path from here, I would probably edge towards the HE-6 as the sound appeals to me more. But the joy for me is the contrast and I can see myself switching between the HE4/6 and the Denon's for quite awhile.