Hi Grinity:
I think you should guide your son through this decision -- and let him make the final decision. Talk to him about aspects of public versus private:
How will he feel about being a grade up from his old friends,
Would he prefer to be at a bigger school with more kids,
What is he thinking will be better about public school, etc, etc.
I think that he's old enough for his choice to be honored if it is well thought through. While every child is different, I made my own decision to subject-accelerate when I was 12 -- I just walked to the counselor's office in the first week or so of 7th grade and said I wanted to go up a grade in x,y, and z. I certainly felt qualified at the time to make the decision and now, in retrospect, I still think I was.
My thoughts are with you and DS!
bk