There are three types of private schools in Mississippi.
True, elite private schools.
These schools are great academic schools (Prep, JA, MRA, etc.) that exist near good public schools. The students at these schools are mostly upper middle class or above, and do not neccessarily attend private school to get a better education (except in the instance of JA/Prep vs. Jackson Public Schools, but those families in NE Jackson could easily live in Madison). I have no problem with these schools - most, if not all of the ones in this category hold the same accreditation.
Private schools that offer a better academic alternative
These schools aren't quite Prep, but most are accredited by SACS and exist next to some subpar public schools (Hillcrest, Brookhaven Academy, Adams County Christian, Oak Hill, Heritage, etc.). Most of these students are there to get a better education, and a good number receive financial aid to do so.
Private schools that remain little more than segregation academies
These schools may masquerade as better options than the public schools in the area, but are not. They do not hold accreditation and are just horrible academic institutions. Again, I may offend someone, but schools in this category include Benton Academy, North Delta and Wayne Academy - there is no reason for these schools to exist other than for segregation reasons.
Have you ever wondered why Lousiiana and Arkansas have schools in the MPSA? Its because the MPSA is the only body that will accreditate them. They could not receive accreditation in their own states. A couple (Silliman comes to mind) have bettered themselves in recent years.