Some kids adapt to changes very well and if you have to move your kid for a new position or family change (divorce) reasons that is one thing. But would you just uproot your child if they have solid social connections and are thriving in an environment just because the popular thing to do is move from public to private or vice versa? There are various reasons to pick one or another, but the best choice is what works for your child and your family. There are so many factors to consider.