Like many other parenting topics, opinions on this issue can be strong and heated. AFAIK, there are no English language studies showing a safety advantage to either type of seat, assuming the child can sit properly.
For my own children, I moved them to HBBs at age 5-ish and 40 pounds (they were both 5 and a few months when they reached 40 pounds). I kept my DD2 in a Frontier in harness mode past age 5 in one vehicle simply because I was too lazy to remove the seat. Shortly thereafter, they used LBBs for travel and carpools (our vehicles have side airbags as do the vehicles we rent when on vacation).
Again on a personal note, for my own children I was persuaded by the Swedish outcome stats (ie., they go directly from RFg seats to HBBs and have enviable road safety stats). Does that mean I tell others (or told in past tense -- my tech certification expired and I won't be renewing) to do so? No. But that was my personal choice.
My girls have never had an issue staying properly in position in their boosters, even while sleeping. I have heard that boys have more difficulty, but as I don't have boys of my own I have no opinion on this either way. I do think it is important for schoolage children to know how to ride properly in a booster seat for carpooling and field trip purposes (our school sometimes has parent drivers for field trips, they aren't always on a school bus). I personally have more confidence that other parents will properly use a booster seat than a harnessed seat -- not to mention, I can't imagine my tiny kids lugging a harnessed seat around for carpooling/field trips, whereas they can easily manage a LBB around Kindergarten age.