I don't think the schools are all that interchangeable. My kids have gone to Churchill. We like it and I wouldn't speak against it. But I kind of wished my kids had gone to Wootton. I think Wootton kids (parents) take academics more seriously-- like they really want their kid to learn and excel. I think Churchill kids (parents) are more into doing what is necessary to get a well paying job as an adult. Those two things mostly align-- nudging kids toward too many AP classes and high SAT scores. But the values seem different.
(But then, we are all kind of stereotyping the school we aren't familiar with, so maybe I'm wrong on that.)
I also keep hearing (on this board) of fights, etc. at BCC. There have been a couple at Churchill, but nothing like what we hear about BCC.
Whitman seems to have a fantastic drama program. Wootton has a marching band. These seem like minor things... unless that's your kid's interest.
Mostly, OP, I think some of this comes down to a tradeoff in neighborhoods, commuting distance, etc. If you move to Bethesda, you can buy a smaller house/much smaller yard for the money. They're nice, but compact. Potomac is more spread out (big yards, no sidewalks). If you work in DC, then your commute will be better in Bethesda.
Note also that they are redrawing boundaries, so before you put money down on a house based on a school, take a look at that conversation. If you buy something within walking distance of the currently-zoned school, you're probably safe. But if not, it's entirely possible that your research will be for naught because the boundaries will change before your kid is in HS.