In his book Education: Free & Compulsory, Rothbard says that education in the South was mostly private, except for some public schools for the poor. The North, particularly Massachusetts, had public schools for everyone with compulsory laws. They were run by the Puritans, so they were Christian at the time. The compulsory laws were interrupted by the Revolutionary War, but they picked back up again in the mid 1800s. This model then spread through the rest of the country.
I do not know about the other differences though.