Curriculum there runs about a year ahead and they are willing to do subject acceleration they were not as enthusiastic about grade skipping but said they would consider it depending on the maturity of the child.
Schools are sometimes reluctant to grade-skip because that may decrease their revenue (one less year of tuition for each grade skip) and/or due to potential impact on test scores (top performer cannot pull up grades of chronological age peers). Are you familiar with the Iowa Acceleration Scale (IAS)? Going through the process with the school may allow them to convince themselves that grade-skipping may be appropriate in some cases.
Schools can also be reluctant to provide meaningful subject acceleration, as that may seem like picking who will be the "winners" on the ACT/SAT, etc, among the cohort of chronological age peers. It is wonderful that the school would consider subject acceleration, and you may wish to learn what form that would take. For example, would your child visit the classroom of a higher grade to join their math class? Would your child work independently or in a small group, on higher level computer-provided curriculum in their regular classroom? Or might your child be expected to choose between joining the regular class lessons or teaching herself without instruction? Would your child complete worksheets?
Does either school have other students who are near intellectual peers? Would the students be grouped together?
I'd choose the school which offers the most flexibility and/or near-peers.
