Surprisingly I did not think it drove the Beyerdynamic T1 (first generation) to high enough levels either. I say surprising because I listen at relatively low levels and the Beyerdynamic T1s are one of the cans listed on the Questyle web site as being driven very well by the QP1-R.
Perhaps it was a lot noisier than I thought, but I would definitely not count on it driving the he-6.
It would be great if someone else could confirm this.
I don't have the HE6, so cannot help at all there, but I tried my QP1-R with both my first gen Beyer T1 and my HE500, and was extremely pleased with both. Personally, I don't feel that the QP1-R "struggles" with the T1. That said, I mostly use it with IEMs, as it's way more comfortable on the go, lol.