It shouldn’t matter either way, but the integrated math approach is new and will have a learning curve.
Private prep schools generally have a better record of placement at upper level and elite colleges, and are far more accountable to parents, have fewer behavior issues, and the kids who attend them are more focused. The downside is that the $ spent might better be saved for college and they lack often some programs at public schools: special ed, elite sports, pools, etc. In general, private class sizes are smaller and the teachers are more motivated (no tenure) and you will get better college counseling as well.
Some public high schools are really good too, but they tend to be magnet or G&T programs.
I’d have your daughter visit and get her impressions.