for what interests and age groups? Private or public? Best for what kind of kid? A kid who likes to go into lots of depth on stuff, or a kid who wants to take in as much as possible as fast as possible, or someone in between? A child with one very keen interest? Or multiple interests? A kid who might resist a lot of homework? A kid who will conform and do whatever is asked?
All good questions. Let's assume either public or private is fine, and that the kid in question is very interested in math and science and in the middle of the (gifted) spectrum on all those other dimensions.
But that said, if you think the answer depends on one of those dimensions, I'd be eager to hear how it depends.
Thanks for all the other replies.