I have mixed feelings in how to answer your request. One of my children went to private Christian school from kindergarten through 9th grade, and the other went from kindergarten through 8th grade. My older one changed to a non-religious private school beginning in 10th grade, and got a top-quality education and had an all-around great experience. (Trinity Valley School in Fort Worth. Too far away for you, but for us, it was worth the commute from Arlington. Wish he'd gone there beginning in kindergarten.) The transition was easy. However, private schools usually do a great job of welcoming new kids, and the the other kids are often eager to see new faces.
My daughter's experience moving from private Christian school to a large, suburban, highly ranked public school wasn't so good. She had expected to be welcomed into the new school the way new kids had been at her private school. She cried every day for weeks. She felt invisible. She heard the "f word" every day. She finally made a good friend in October (also a new girl) and she brightened up considerably. By the end of the first semester, she was happy to stay there, and she loves it now. However, she is coasting. Rarely any homework, making A's with a few B's.....it's too easy. There are racial tensions, which dismay us, since the races mixed very, very well at her Christian school.
The benefit for her is that her high school has a well-developed art program with AP art. Her old school only had one art class. This will be her career. She is a senior now, and is being courted by the country's best art colleges, which probably wouldn't have happened had she she stayed at the Christian school.
However, I have a major, huge, tremendous regret with both children about changing schools: It undermined their faith. They probably would have gone through the normal teenage questioning that many people experience, anyway. However, at a Christian school, there is peer pressure and lots of support for staying more on the straight and narrow path. Many of those kids turn away from their faith after they graduate, but it is well ingrained until that time. (But you also need to realize that some of the kids at private Christian schools are ones who misbehaved at other schools, and their parents put them there hoping that it would straighten them out.)
Both of my kids made a lot of friends in public school and the other private school who are nice people, but who don't care about church or faith at all. This has seriously undermined their own faith and commitment to participating in worship and youth group. If we were to do it over again, I don't know what I would have decided. Knowing the danger of having my kids become apathetic about church would have probably scared me away from making the change. On the other hand, both kids have college opportunities they probably wouldn't have had at the old school (also a good school, but can't be all things to all people) or through home schooling. Salvation is eternal, the rest is not. Peer influence is super strong for most kids at that age.
If you do decide to send your kids to a non-Christian school for high school, make sure you attend a church with a great youth group. We did that at first, but then the pastor left (main minister for a really great new church now), most of her friends there graduated, and so my daughter stopped liking the youth group. Until that time, many of her friends were part of a girls' bible study together. They graduated, the youth pastor left, and now my girl is adrift. So, the problem is really more a matter of not having religious peer support, which doesn't have to come from school.