I never went to private school (my parents couldn't afford it) but I did attend several alternative schools and schools geared towards students with learning/developmental disorders. I would say the specialized education was very helpful to me when I was a child and needed support from others to understand and advocate for myself properly, but less helpful as a teenager when I had learned to manage most of my difficulties on my own and mostly just wanted to be like everyone else. I ended up attending an ASD-specific program within a mainstream public high school where I could access support while taking regular classes, and that was a nice balance for me.