We moved to Mok-dong, but is a general high school really better than an autonomous private high school?

I met a friend yesterday whose son is a high school sophomore.
They said it has already been five years since they moved to Mok-dong for the school district.
The youngest is entering college this year.
After listening to a long conversation about schools, academies, and GPA rankings, a thought suddenly occurred to me.
With the child's academic ability, they could have gone to an autonomous private high school (Jasa-go) like Baejae High School or Boin High School near their original neighborhood; was choosing a general high school in Mok-dong really the better option?
Especially since their workplace is in Gangnam...
I heard that competition for GPAs in Mok-dong general high schools is quite intense because there are so many high-achieving students. If they are going to face fierce competition anyway, wouldn't it be better to receive the curriculum and college entrance guidance provided by an autonomous private high school?
Is it truly the best decision to send a child who is capable of attending an autonomous private high school to a general high school just because Mok-dong is considered a good school district?