I actually gave some very detailed information about the 4 schools you mentioned in another post that for some stupid reason Letsrun decided to delete. Insanity. It actually had some info you sought, and I actually did some research for you to write that post.
I'll be VERY brief about what I wrote about the 4 so as not to upset the baby monitor who deleted my other post.
AIS: Non-religious and is open to and supports people of all religions, race, sexual preference, etc.
Westminister, Lovett, and Pace are all Christian schools that have Christianity at their core. If that's for you, then fine, but if not, then perhaps not fine. Too many discount this when looking at private schools.
The ONE that seems to have more of a singular focus on academics is AIS. If I were in your shoes, and I HAD to pick one of those private schools, I would pick the one that isn't bogged down by religious ideology...and that one is AIS.