I have a HE-6 setup that sounds good although not optimal. I still wouldn't say the HD800 is the clear winner among the two. It's comparable depending on which sound signature you prefer. Once the amp gets better the HE-6 moves ahead of the HD800. I've heard the HE-6 with speaker amps so I have a good idea what they are capable of. The HE-6 imo is the safer choice of the two in terms of sound signature. The HD800 is more risky since the treble is a big complaint as well as it doesn't have that much bass
Also the HE-6 and it being thin should not be in the same sentence even underamped imo. I've heard it with amps of varying abilities and I've noticed that the treble is more the issue than the bass.