I haven't seen a HH roll at all, but then again, I'm up top. I'll investigate that next time.
What about efficiency/ strength loss?
I like that it won't turn into an overhand knot, but simply fall apart when slipped off the end. When rigging short pieces, I don't have them untie the bowline, when possible, just slip off the end, and I can slip it back on the next piece to skip a step. My 9/16" dbl braid has a large spliced eye, so I can slip a bight through, 'invert' the eye, and have a clean girth hitch, to the same effect. Also, I don't have to have a stopper knot put into the end to prevent it from running up and through the block on the return trip to the top.
A minor individual preference
Many people don't have a spliced eye on their rigging line, but I got one. It gives a stronger pulling point when used to pursuade a tree to the lay and is slightly cleaner for knotless rigging, as well as stronger. I don't have a 5/8th line to move up to, so knowing I have most/ all the strength of the 9/16"s is good in my mind.