In your opinion, How does teaching in a private high school compare to teaching in a public high school?

Generally, teaching in a public school is more specified by credentials/licenses issued by the state (in the US) and requires adherence to a specific curriculum (usually tied to state and/or common core standards) and standardized assessments. Private schools are likely more concerned about actual experience rather than a license and use their own assessments (though there are often assessments for entry, the ISSE, which almost never happens in public schools). Also, special education private schools are rare unless they are funded through public school dollars. Private schools almost never accept special education students (unless they are specific for special education funded through public schools). Private teaching usually involves smaller class sizes, more time to prepare, but fairly strict adherence to a quick turn around of student work. Public school instruction usually has a large teaching load (unless for special education which has strict class size limits) and instruction is very strictly determined by a union contract.