I agree that either math program woudl be fine. As part of the process you can try to meet with guidance counselors at both schools to see where their students end up for college. In the end, I’d choose the school that is the best fit for your D – if money is an issue that would lead towards the public school route.
And as an aside, I’d caution you or your D against singling out a few specific colleges as targets before she even sets foot into HS. Things can change so much over the next couple of years.