Private or Catholic School?

Well my husband Jason and I make a substantial amount of money now and we've balanced our income with our expenses. Now, we are looking into either a Private or Catholic School for our three out of four children, Michael (9), going into 4th grade, Anthony (6), going into 1st grade, and Juliana (4), going into Preschool. Now we are looking at both Private and Catholic. We are Catholic, but aren't sure. Has anyone had any experience in either? We are planning on having more children in the future as we are stable, and would want more, so we need a substantial school. What are the benefits of Private or Catholic School??