I don’t really think it has to do with perceived value or quality. I think it’s just a matter of proximity. Unless something is so much better that it’s worth the hassle of flights and only being able to come home at holidays most families are going to choose the local or semi-local option. It’s not just that New England has a number of rigorous boarding schools, it also has schools for a wide variety of kids, everything from kids with 99% SSATs to schools for kids with severe LDs. Among some of the kids I know who went out of area were a serious horseback rider, a triplet who wanted to be at a different school from the other siblings, a kid who attended a school headed by a relative, and one who needed a therapeutic school.
Of course there are kids without special needs or interests who find that there are curricular or other features to a school that just fit them better, and sometimes kids have more success with admissions if they’re willing to venture outside their geographic region. I certainly don’t think New Englanders look down on schools in other parts of the country.