Benefits of private primary school?

Looking for thoughts on whether private primary is worth it. I’m on the fence. Background: live in the catchment of an outstanding primary school with a similar 11+ pass rate to the local prep. The main differences are facilities and class sizes (15 vs 30). We can make private school work but with no fat left: tied to a high stress and highly paid job,no nice holidays,minimal savings etc .

Has anyone else been in this situation and what did you decide to do?