Interesting thread. I'm very-low-carb and quite low-fat. Most of my fat comes from cheese, avocado, olive oil (and oil-marinated olives) and meat. I seem to be thriving, energy-wise. I was indeed extremely hungry for the first two months of this diet (mid-February through mid-April of this year) but the hunger largely went away and I attribute that to the recovery from carb addiction.
The hunger returned recently, but less extremely, because I eliminated copious nut snacks from my diet in an effort to prevent further kidney stones (another story, not for this thread). I have so far dealt with the hunger simply by "eating more" in general, and even adding a single square of Lindt 85% chocolate daily (about 4g carbs).
Members of this forum frequently advise me to increase the fat quotient, which I haven't yet done, but accept may be the right way to go eventually. (I am on the edge of "underweight" as measured by BMI but don't attach much significance to that. See signature.)
(Edited 10 minutes later to add a few more details of my diet.)