Also keep in mind that your guidance counselor will send a “School Profile” (for both schools) along with their recommendation.
It includes things like Average SAT score, how many Merit FInalists there were, how many AP courses, average scores on AP tests, and what courses are offered.
So if they see you went from a place with an average SAT score of 900 to one with 1200 then they will see this new school is more challenging and put your info in context.