I go fat side down
I have done both, and have had good success with either. However, I've gone to fat side down mostly because any fat rendered on a fat-side-up cook doesn't go into the meat, but rather runs down the sides to the lowest point and takes some of the rub with it along for the ride to the bottom of the pit. I've had better bark with fat side down.
LG BGE-Brinkman Cimmaron-Custom Pull-behind (old grade school boiler)-Weber Kettle-DCS 30"