Some other reasons might be smaller class sizes (individual classes and total in the grade), daily religion classes, different specialized classes and opportunities, more rigorous AP classes etc.
Obviously the stuff above varies from school to school, but in my case all of the above was true for the private Catholic schools I attended in Houston.
Currently, my kiddos attend public schools, but that may change as my hubs and I evaluate each school individually as they age. For now we are happy with ASE, but we will evaluate the Jr. High options once they are older.
Another reason we haven't gone the private school route is that lack of a Catholic high school in the area. I would hate to start private school in this area, and then have to drive (or let them drive) to and from St. Agnes or Strake Jesuit (located on Bellaire Blvd between beltway 8 and 59) daily from this end of town. If we feel like we need to go this route, we would probably consider moving back into Houston.
It's a lot to think about, but luckily we are several years away from having to make hard decisions....