Fairfield Country public high school vs Greens Farms, RCD, other day schools

Forgive me if this is the wrong place for this–

I would love some honest feedback about high school choices-- public vs private. I have a 7th grader who’s at a private school now, but she’ll leave for 9th grade to a high school. The academics at our public are considered to be excellent and the school offers academic and extra-curricular programs that would be great for her. She’s likely to be in AP/honors classes. The school is close by, convenient, and it is well-regarded and supported in the community. But then we see the bright shiny objects around us like GA, GFA, RCD, etc. (Hopkins would be great but I think it’s just too far and I don’t even know about admissions). What is the value-added for all the extra time and $$$ for the private schools? (I know some, being in private now, but want to hear YOUR views). Please share anything even remotely related to this quandary.
Many thanks!

I go to Fairfield Country public high school and I love it. I exposed to a challenging curriculum, passionate teachers, and competitive sports facility.