I'd like to share my own personal anecdote from going to a Catholic school in Saskatchewan for 3 years, despite not being a Catholic.
I moved to Vancouver after a few years in Saskatchewan, and I went to what was considered one of the best elementary schools. The difference in quality of education was pretty startling. We covered far less advanced topics, had no freedom to do additional topics without significant paperwork and meeting between parents and teachers and staff, and the classrooms were in general much more overcrowded and underfunded.
In short, the education I received in a Catholic school in Saskatchewan was far more liberal, progressive and of higher quality than what I received in a public school in Vancouver.