CA and Middlesex are considered to be rival schools, and as such, they have some stark contrasts. I’d say the greatest of these is political view. CA is a well-known left-wing school, but I can imagine MX to be more politically diverse. Once again, either school is a world-class facility.
They’re not really rivals in the traditional sense, mostly because they’re not in the same sports leagues. CA is in the EIL and Middlesex is in the ISL, the stronger league. IME most kids at the two schools recognize them as different, although some applied to both. Middlesex’s traditional rival is St. George’s.