My son, as Grinity knows, is very close in age to hers. I am dealing with a twelve (soon to be 13!!!) year old seven grader.
From pre-school through grade 4th he was at a private, religious school. Considered best in our little town. Had some great teachers, had some awful ones too. The absolutely worst one was his third grade teacher.But we stayed around one more year.
Ghost always "hated" school. He never put it into words, but there was this constant anxiety in the evenings and some mornings, sometimes he would cry for no reason at all, the anxiety was so overwhelming to him. But at school he was always a proper boy, no behavioral problems, always getting highest marks for his conduct. Looking from a perspective , I believe that the anxiety was caused because they were trying so hard to put him into a box and the process of fitting in was so very painful to my son.
Angry sounding young boy - I can relate here totally Grinity, althought my son is not as verbal as your seems to be .
I agree that private school has given my son good study habits, he is used to wearing a uniform (current public also requires them), used to turning his homework in, finishing assignments etc. Yes, there is no "hand holding", but it is probably giving him more independence and forcing responsibility on.
As you know from previous posts, my son is thriving at the public school. He has been allowed to be himself, and his social site has been blooming. One notable difference in our stories is the fact, that for us it was a public school that has recognized my son's ability and offered above grade level work. Our private school was just patting me on the back saying that I have a great child. For you the reverse is true. Please do not forget that!
Middle school is a very difficult time. I agree that listening to your son is a good idea. However, is moving now, just for one year, the best idea? How likely is it that if you choose public HS, he will stay with the friends he is going to make in 8th grade? Will the middle school allow for above grade level work in school?
Grinity knows very well, that you have to take it one year at a time. Last year was great, this one not so. Is this the main reason you are considering the move? Do you know what the curriculum is going to be like in public?
Every situation is different, but from my perpective here is a little comparison:

Private School
+ uniforms
+ discipline
+ school was religious, did not have to take son to religious classes in church like we have to now.
- too much time was spent on religion, taking away from core curriculum
+ my son's handwriting was great, teachers were really paying attention to details
- too big emphasis on sports
+ parents cared a lot about their kids education
- kids from very affluent homes, some hispanics at school but they were not really treated equally
- principal was absolutely "non approachable", anything you said might have been taken against your child
-not recognizing the need for differentiation and acceleration
-my son was bored
-no foreign langauage


Public School
+ immediately recognized that "something needs to be done with this child" in terms of acceleration and differentiation. They offered an immediate grade skip which we declined - he had a great 5th grade teacher with G/T experience.
+ uniforms
+ foreign language
+ teachers from all over the world, speak with accents (important to me as I also have one)
+ kids from very different backgrounds, very different financial situations
- parents less involved in their kids education
- my son's handwriting is horrid :-) I have actually started looking through his notes and am assigning him things to re-write. I know he can do it, because he used to do it!
+ school rewards academics, difficult to have straight A's
+,+,+ - my son is thriving, he is very popular, vice P of student body.
+ principal and therefore teachers listen to parents.
+ able to provide in school acceleration.

Grinity, if your son insists on public and you are leaning towards it, why not try it for a couple of weeks? If you are dissapointed, I bet the private school will take your son back one month into the school year?
I know those are very gut wrenching decisions and as I have said
every situation is so different. In our case, changing for the last year of middle school would not be a good idea, since most likely Ghost will go to HS in another city.
Good Luck!
Ania