Which should make no sense because the teachers themselves work odd years in one school, even years in the other school.
Peers make a huge difference. Before university, I split my high school between two schools - one that was near the top academically, and one that was quite poor. The latter did have some smart students intellectually, but almost none did well academically because it wasn't valued by their peers.
Then I went to a very average state university for undergrad, and a top school for graduate studies. The difference wasn't that high in terms of teaching (the average school actually had much better teachers, but offset it by low expectations). The real difference was in the peers.
You like engineering? You like coding? Want to do some cool side project? Very hard to find someone like you in that average university.
Then when I started working, I started tutoring some middle school kids. The kids seemed totally capable mentally, and I was trying to figure out how they can't retain simple facts like number of months in a year. Until finally it hit me. They don't have problems learning things. It's just that no one in their orbit (peers or parents) care if they know these things. When I was a kid, I'd be an idiot amongst my fellow students if I didn't know it. So I did. Everyone did.
But if you're around people who think it's OK not to know how many days are in a year, chances are you won't know it, no matter how intelligent you are.
I strongly believe that peers are important and choosing school based on the type of peers is a valid choice. As another (more positive) example, we live in HK in a multilingual family (I speak French, my wife speaks Cantonese), my son goes to an international school in English and Mandarin. Most of his classmates speak at least 2 languages, many speak 3. In that environment, it's easy for my son to see value in speaking multiple languages and he's never rejected one language. I have a friend whose daughter is in France in a monolingual school where her peers don't value speaking multiple languages. As a result she's ashamed and refuses to speak Cantonese.
Or maybe Cantonese is less fashionable in France than French is in Hong Kong?
The finding here is, competitive parents have an impact on the college approval rates of their children. Get them to all send their kids to the same school, that school gets better approval rates, regardless of the teachers.