While this is not necessarily the best analogy, in easy layman terms think about how big the drivers are in the HD800 compared to the armatures in the SE535. These drivers need power in order to push air and make sound. The amp is like an engine in a car. If you take the engine from a BMW M5 and put it in an 18-wheeler, you could probably still make it move, but it would not be ideal.
I have owned both the W4 and the SE535s and I agree with you that the SE535 was more engaging and emotional. The W4, while impressive on a detail and technical standpoint, was frankly boring and unemotional to me.