I’m not sure about what towns MX will allow to apply for day slots but I’m sure there are no restrictions for CA applicants.
Some differences:
CA is 50-50 boarding/day students, MX is 70/30.
CA is right in the middle of town and within a very short walk of the commuter rail train. A lot of kids take the train to and from school. MX is about 2 miles from the center of town. No one takes the train. It’s much more isolated and self-contained and has more land.
MX requires that all freshmen and sophomores participate in 3 seasons of interscholastic team sports. They do consider dance (offered only in the winter) a team sport. Juniors must do 2 seasons, seniors 1. In addition to competitive teams sports CA students can fulfill their afternoon requirement through dance, intramurals, phys-ed, the play or community service. CA has a well-known and well-regarded modern dance program.
CA doesn’t do awards. MX does.
CA tends to have more square pegs or artsier kids. MX is more traditional. This is a sweeping generalization and while you may hear from MX parents (correctly) that MX has strong arts programs, and from CA parents that there are plenty of traditional, sporty kids at CA (also true), I can pretty reliably tell a group of CA kids apart from a group of MX kids when they’re in town.
Both have rigorous curricula and excellent reputations.
IIRC, it’s easier to switch from day to boarding at CA than MX.
MX has more of a dress code than CA. For instance, CA students can wear sweats, MX students can’t.
At CA every senior does a chapel talk. Every MX student takes AP English as a junior and MX’s writing program is excellent.
Here are the student handbooks for each school.
https://caconnect.concordacademy.org/Family_Resources/About_CA/2016-17_Student_Handbook
https://docs.google.com/viewerng/viewer?url=https://www.mxschool.edu/sites/default/files/uploads/7_2016handbookfinal.pdf
I would not say one is better than the other, but often one is a better match for a particular kid. I’d encourage you to visit even if you aren’t able to schedule a formal interview.