I would agree with PP. I think what happens with WJ, BCC, and Whitman with the stereotypes is that families end up reinforcing it. For example if we were driven by the best test scores, we would have picked Whitman hands down. I was worried about diversity since my kids are bi-racial. I wanted that balance that they can relate to people with different backgrounds similar to what will be found in the working world, but at the same time have enough of a peer group to feel comfortable in their own skin and not feel they have to either prove something or missed out on part of their heritage. For us, that ruled out Whitman and left BCC or WJ. We happened to find a house we liked in the WJ cluster first. I do see BCC as being a little more sophisticated between the location in downtown, having the IB program which emphasizes that international perpective, and having more of an socio-economic spread than WJ.
You may want to look at each school website to see the school profile, special programs, clubs etc., there may be something offered at one school that falls into your child's interest that isn't offered at another school like the IB program at BCC.
Also you may want to see if one school over another would offer an easier transition for your child. I transferred in 11th grade to school in another state and pretty much my classmates had been friends since kindergarten and really had no interest in new friends. I had atleast people to eat lunch with by my participation in extracurriculars but it was a tough road.
Here are the websites for the schools:
http://www.montgomeryschoolsmd.org/schools/wjhs/
http://www.montgomeryschoolsmd.org/schools/whitmanhs/
http://www.montgomeryschoolsmd.org/schools/bcchs/