Call the schools your family is interested in, and ask them which they prefer. If they won't say, ask them which the kids who 'usually' apply 'usually' take. You want to make it as easy as possible for the school to get to know your child, so make an effort to speak their language.
Ivy Leaguge applicants "usually" take the SAT, but the schools use a table to convert from ACT scores to SAT scores, so I don't think submitting an ACT score handicaps an applicant. I wonder if something similar happens for private high school admissions.
