Hello there, my son is 14 and was diagnosed with autism, ADHD and dyspraxia at age 7.
A lot will depend on how academic your son is and how difficult or not a private school would be for you financially,
Definitely the state sector have much greater input in the primary years and my experience of this has been good. My son was extremely well supported during those years. However I have spoken to others who haven't had the same experience.
Secondary school was a nightmare for my son, even the smallest school in the town was too big. Coupled with a SENCO who was lovely but totally ineffectual.
I went to war with the local authority (or at least that's what it felt like) and my son is now in a special school and thriving. However he won't be doing GCSEs there as they just don't offer those. He may not have reached those even in mainstream.
When I was looking at the private sector (I could have fought the local authority for a private placement if no state provision could be found) I found relatively few special schools local to me. The ones I did find looked fantastic though.
I am hoping someone who has used private schools will post here and tell you their experiences. But for me the State sector was fantastic...up until secondary provision.