Less competitive, at least in my state. The higher paying public school districts have a lot of applicants, who are often more senior and have either higher degree levels, or degrees related to the subject they would be teaching. The parochial schools are seen as being somewhat of a stepping stone for new teachers or those who are trying to get a foothold in a desirable location.

My secondhand understanding is that they make up for it by offering more control over the students, down to selecting and expelling them.