LAA is more flexible with a kinder/gentler director. CHM is the strictest kind of Montessori with a rigid/inflexible director. Very different schools, but each might be good depending on your child’s personality and your goals/desires.
If you have geographic flexibility, maybe consider McLean Montessori and Brooksfield School, which are on Kirby Rd just east/west of Old Dominion. So not far from north Arlington.