Really and truly, it's according to the school itself. Christian school means two things - private where people have to be able to afford to send their kids, so there aren't a lot of lower economic families there, and the school can say no to any kids who don't meet their criteria - ie behavior problems or learning issues. The second is religious - the type of religion that the school pushes, which can be liberal all the way to evangelical conservative - so if your personal beliefs are really different than the way the school leans, it can be hard on your child. And between all this, there is usually not a lot of diversity.
Now, that said, it can be much easier for you to navigate a smaller school where there aren't a lot of or any at-risk kids, so the teachers are focused on teaching rather than disciplining.
Here's the other side of it. If your child has any learning or behavior difficulties, the private school can say goodbye to you and your child, because they either don't want to or don't have the ability to work with special needs. A public school that is worth its salt will put together an IEP for a special needs child and get them extra help to keep the child on track. It can be a godsend for your child, IF you have a committed teacher and staff - but even with the best IEP, if the teacher doesn't follow it, it isn't worth much.
Regarding the religious aspect, just because the school is Christian doesn't mean that it is a good school. My mom was a public school first grade teacher for over 20 years and loved teaching. (She is also a devout Christian.) She taught in a low school in the bad part of town because she felt those at-risk kids needed someone who would love them and challenge them - I respect her so much for that. We didn't attend the school where she taught, but at one point she decided to put my younger sister in a Christian school because people talked so highly of it. Just months into the first semester, she knew she had made a mistake. My sister wasn't learning anything - the teacher sent home assignments and notes with poor grammar, misspellings, work that was far too easy for the grade level, etc. My sister lost a year, so to speak. My mom thankfully understood what was happening, since she was an educator. She moved my sister back to the public school and got extra help for a while to get her caught up.
So really do your homework before making a decision. I was overseas for 6 years and had my children in a private Catholic international school whose academics were very rigorous. I loved that school, and still do. But we were lucky. Coming back to the US, I have put my kids in a public school, and they are doing well.
All my best,