Disadvantages: Some, but not all, of these schools struggle with funding. Tuition costs are often less than a prestigious private school, leaving less money available to provide the technology and special classes that you would find available in a public school or a prestigious private school.
Although the school is 'religious' in its nature, it often is operated very much like a public school in its use of curriculum. You should carefully examine the underlying foundations of educational philosophy. The content of curriculum (excluding Bible) is often secular.
Although many parents enroll their children in these schools for religious instruction, very often people enroll their children in these schools for a supposed safer environment, and a perceived idea that the quality of education must be better than public education. This may not be a realistic belief, or be in alignment with the established purpose of the school.