Hi Paul:
Chinaberry (Melia azedarach)is in the same family as mahogany, the family Meliaceae, and the wood should be fairly stable when dry and behave not unlike mahogany. It will likely be a bit more pale with a more pronounced figure. I don't know if it is also photosensitive like mahogany is, so I would try a quick experiment to cut some wood (face grain), cover half of it with some aluminum foil, and leave it exposed to sunlight for a few days. If it is photosensitive, the exposed area should be considerably darker than the covered portion. I have not turned it myself, but have seen some nice projects made with it. NOTE that the SEEDS and LEAVES ARE TOXIC.
The Popcorn Tree is probably the same as the China tallow tree (Triadica [Sapium] sebiferum), a relative of the poinsettia (Family Euphorbiaceae). I know it as a potential US invasive species (native to E. Asia), and a plant that has some potential for use in producing biodiesel from its waxy seed surfaces. Given that it is a fairly fast growing tree, and is related to euphorbias, I don't think the wood will be particularly dense or that spectacular as to figure (....if it is please let us know). As with many members of the euphorbia family, the sap of the tree should be treated as potentially toxic; avoid contact with skin, eyes, mouth, etc., since some members of this family can produce reactions of contact dermatitis or worse.
Hope this helps!
Rob Wallace
(Botanist at Iowa State University and woodturner whenever I can....)