The answer to that question really depends on your particular family situation. Homeschooling has been pretty successful for our family. There are tons of resources available that allow your child to accelerate and engage with material at her own pace and level in a way that is a lot more flexible than most schools would be.
Private school didn't work so well for us, as they didn't really have the resources to give our children what they needed in terms of supports for 2e issues, acceleration for giftedness, or even providing a meaningful peer group, but your mileage could certainly vary on that.
