A friend recently pointed out an interesting article from the Jewish Week that touches on this point, albeit in a different context, that of special needs:
In short, there is a tension between our demands that our Jewish day schools be able to compete with Sidwell Friends and Choate, while deeply covering Jewish subjects, as well as comprehensively addressing special needs. There is no way around it. [...]
When I was a kid, and went to Jewish day school, my parents made a major financial sacrifice, and accepted that they were not going to get 100 percent of what they wanted from one school. I got a decent Jewish education if not the best secular education (I did supplemental work with my parents and a tutor out of school) but on balance am grateful for the experience. It was compromise, and a lot of my education -- Jewish and otherwise -- but the goal was to imbibe the mesorah and to participate in the construction of the next generation of the Jewish community.
No school will ever be perfect. As parents, we need to determine which school is best for our children; for some, that is the school that is the most like them. For some, it is the school that provides the most specific approach, for others the most open approach; for some, it is the school with the strong Judaic or secular education; for others, it's the school with the best middos, or some combination of the above. And for many, it's "Which school can give me the best tuition break!?" All of these are valid approaches when applied correctly.
For us, though, it was less about a specific trait than about an approach: What aspects of our children's education are we least and most equipped to supplement? I bumped into an older supporter of one of the schools whose children had gone to both, and who had grandchildren in both as well. The first words out of his mouth were that I was making a mistake, and should definitely send the girls to the school that we had not chosen. (He is nothing if not open about his opinions.) We ended up having a fantastic, if quick, conversation on the subject, and he noted at one point: "I will acknowledge, [the school we picked] does a fantastic job of ingraining X." For us, it is easier to supplement our child's (say) math education than supplement X - and therefore, we chose to put ourselves in a situation where we can supplement any potential problems.
By placing children in schools which match the parents, while it helps with consistency, it also can create a redundancy - both positively and negatively. While the school's strengths may be further enhanced by equally strong parents in a given area, any lacking the school may have would only be compounded by the parents lacking the same. But by viewing the school more as a teammate in a child's upbringing, where the strengths of the school and the strengths of the parents help overcome one another's deficiencies, it can help a child become a more complete person.