I've made many arrows from privet and I think it's better in compression than tension. That means that you will probably get the best performance if the back is flatter and wider that the belly. But since the stave is really long, I don't think it matters much. There won't be too much stress on the wood if you make a tall bow.
Cherokee bows, from what I've seen, were mostly man-sized bows with a flat back and belly. They were usually D-shaped bows with no "built up" handle. They bent in a graceful, continuous arch at full draw.