In my experience, the amplification that this adapter provides is not enough for larger headphones.
Asking him about it, he pulled out a new Pixel and said it was for op's very reason. In particular he noted that the pixel had a much better DAC than any one iPhone he'd ever had - and in particular that it could drive all of his higher end headphones. He also mentioned that the new iThing adapter has it own DAC inside the adapter... it's apparently powered by the lightning port with its own drivers - and that he had tried it out anyway but found it incapable of properly driving any of his nicer headphones.