R.R.
I work in a private school. We are members of the National Association of Independent Schools. (NAIS) You could go to their website, http://www.nais.org/. OR - if you are looking for specifically Catholic schools or specifically Episcopal Schools, Google "catholic schools, city, state" (you didn't say where you were moving, which might help if we knew that).
Private schools are usually members and/or accredited by different organizations. If there is one in your current area that you like, go on their website and see what organizations they are members of and search THOSE websites. Logic would dictate that they would do some comparing of test scores, attrition, college acceptances, etc.
Good luck!