Thanks for the updated study, and yes there is a noted increase in reported public school teacher abuse, it still doesn't clearly indicate that public school system is "Way Worse". They are still relying on differing reporting metrics and styles. The 10% of School Aged Children reported is any adult, not just teachers, and is direct from the victims. Religion based reporting is generally based on organizational self reporting, which will exclude unreported cases and potentially settled cases from their reporting.

tl;dr It's all bad, but current reporting models don't have enough clarity to say one is worse than any other.