I moved from Vienna (at the time probably middle class rather than upper middle class) to Mclean (solidly upper middle class, with some rich people). Mclean schools were full of upper middle class kids. The high school parking lot had Lexus/BMW. Lot of smart kids and many who went on to be pretty successful, but also a lot of arrogance and disdain for "the south," "the rest of Virginia," and "flyover country." The attitude was such that I didn't even realize Chicago (a huge city not on the coasts) existed until I was in college.

I can't say I noticed any difference in the schools. Mclean had great test scores, but that's because it has managed to zone out almost all the middle and lower-income people and the working class immigrants. My wife and I have been struggling with where to send our daughter to school. I don't think it's worth it pay a big premium to buy in the higher-ranked school districts. Unless the district has an actual gang problem, it's generic "McEducation" almost everywhere. If our daughter shows tendencies of being a creative thinker we'll likely do private for at least high school. If she shows a high tolerance for petty tyranny we'll likely do public somewhere in Anne Arundel (which is close to DC but far enough away where she might meet some blue collar people).