Wow! That is a good question and a complicated one. Really, there is no single answer. There are a number of factors involved in choosing which type of school is right for you and your child, whether it be boarding, Montessori, Christian, Catholic, special needs, IB, or gifted. The key word really is 'benefit'. What will be best for your family, your child, your budget. To simplify, here are some questions to ask yourself when deciding whether or not to choose a private school option.
In many areas, you pay your education taxes whether or not your child attends public school. However, some jurisdictions do offer tax breaks for parents whose children are attending private school.
For some parents, this is the key to a private school decision. If you wish to have your child receive a religious or culturally-based program, then private school is your best option.
Many parents of private school children have made the switch because they are looking for smaller classes, a specialized type of program (such as for special needs), or a specific academic focus. Unlike public schools, private schools can control the number and type of children who are admitted. They can require admissions testing, and are able to expel students whose behaviour or academics to not meet the standards of their institution. On the other hand, students who go to public school are exposed to a much wider demographic, both culturally, academically, and socioeconomically.
All teachers in public schools in almost all states and provinces in North America are required to have some form of federal, state or provincial certification along with a bachelor's degree. In the more prestigious private and boarding schools, there are likely to be teachers who are much more highly qualified, with graduate degrees and higher level awards.
Private school and public school administrators and educators all do their best to create the best learning environment possible. There are excellent public schools and there are excellent private schools. In Canada, the Fraser Institute ranks schools, often finding favour with private schools, although it does highly rank some public schools. In the USA, the situation is similar: there are good public schools but many of the best overall schools are privately funded. A study by Harvard University found that private school students averaged higher than their public school counterparts in standardized tests in 11 of 12 comparisons of students.
In summary, as a parent, you need to decide for yourself which option fits your child best. Talk to administrators, visit the schools, see what the program and teachers are like, and ask plenty of questions. Having options in education means that every child will receive the education that suits their needs, learning styles, parental budget and values. Good luck in your search!