In the state of MI, where I am, they do not have any budget for gifted programs in the public schools either. So, in MI, if I were to switch from public to private school, I would want to make sure that the private school I was selecting was actually targeted towards gifted children and offered a range of gifted services. I believe you can find a list of gifted schools on the Hoagie website.

http://www.hoagiesgifted.org/schools.htm#susa

If it is not a gifted private school, I would compare the curriculum to the public school. If it is similar, then I see no point in changing. If it is a lot more challenging, then it may be beneficial to pay the tuition and switch.