My DH and I each went through 12 years of Catholic school. We started our DD (17) in a private, Christian school because there weren't many Catholic elementary schools in our area.
She continued in Christian schools until she reached 5th grade, when we moved to an area that didn't offer any. Then she started public schools.
It was a big change because they didn't have the discipline and structure. I remember her coming home the first couple of days saying kids talked aloud in class, they were free to roam the classroom, etc.
She continued the next year to middle school (6,7,8) and now she attends a public high school and is a Junior. We weren't crazy about the middle school, but I think it was more the age bracket she was in and not so much the school itself.
She now attends a public HS, but is in a Medical Magnet program as she will be pursuing a medical career in college.
Overall, it was not too big of an adjustment to her/us, but it there were differences. Nothing we/she couldn't adjust to, though. Good luck!