I went to Private/Catholic school K through 12th Grade in Baltimore City and my husband went to Public school in Baltimore County. We sent our daughter to Private/Catholic school K & 1st Grade in Baltimore City. We switched her to public school in the 2nd grade after we moved to Baltimore County. The decision to switch to public school was not made overnight. We visited the school, toured it and had our list of questions ready for the administrators. We were very pleased with the facility and the responses to our questions. It was a huge adjustment for me because all I knew was Catholic school, but by the end of the first year, I was completely comfortable. Our daughter now attends a public middle school and she's doing wonderfully. All public school teachers she has had have been very educated. She has been in Gifted and Talented classes from the start. It has been a tough curriculum, especially now that she's in middle school.
I understand your concerns as I had the same. In my experience so far, I have found that horror stories will happen in both private and public schools. Fortunately, we have experienced very few horror stories. I was (and still am sometimes) nervous about the middle school years. My saving grace is that most of my daughters classes are GT. In those classes, they need to work and work hard. There's no time for fooling around.
As far as education goes, in my experience with my daughter, public school has it all over private school. However, it could be the opposite depending on where you live. If we still lived in the city, my daughter would most definitely be in private school.
Overall, I think you should visit all the schools your considering, request tours of the schools and have questions ready. Tell the administrators your concerns. The feedback you receive will weigh heavily on your decision - I know it did for us.