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If money is no object, either of these would be fine choices.
Just living in UA takes loads of money in and of itself, so what you've got with UAHS is a pretty de facto exclusive school, even if it is public.
At Academy, you'll truly find the upper crust from all over Central Ohio sending their kids there. It used to be all-boys, but went coed in the '90s. It has long been regarded as the premier private school in the Columbus area.
Academy probably draws a more culturally, religiously & ethnically diverse group of students—with the one commonality being massive family wealth. Upper Arlington is more homogeneous ethnically since it's a self-contained suburban area, but its socioeconomics are more variable (not everyone in UA is rich; some families just break their budget to live there so their kids can attend the schools).
As for college prep, I would concur with YoMikey's assessment above: Academy = pre-Ivy League.
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