First, please don't feel like a failure. I think you are making the best decisions you can for you, your children, and your family. The fact that you were willing to look at the situation, figure out what was not working so well, and make a change is a great, wonderful model for you to set for your kids! Give yourself a big pat on the back for showing that people should be flexible and use new learning to approach problems and always keep learning about yourself.
Schools are really, really individual. Some public schools are great, some are less so. Some Catholic schools are great, some less so. The only way you will know is to go and visit, ask lots of questions, use all of your senses to get a true feel of the place, then make a decision based on those facts and your family's values. Having any of us tell you what schools around us are like probably isn't very helpful, unless some of us live close to you -- I can tell that I live in another world!
I am very blessed in that I get to send my children to a private school that I worked at when I had my catering business for about 5 years. So I know really well what a regular, day to day student life looks like and have as much confidence as possible about a good fit between school and my kids.
Go and visit the schools you are considering. Talk to the people in charge. See if you can get into the grade-level classroom(s) you will be in next year and observe for a period of time (longer than 5 minutes). Ask yourself if your child would fit into what you see. I suspect people here would be more than happy to help you formulate a list of questions that you should answer (by talking or by observation) to help you decide.
Also, remember that sending kids to school doesn't take you out of the loop. Not only should you be involved in their school, but you still have a lot of time and control over what they do outside of the classroom. If Christian teaching is important, you can plan ways to accomplish that, even if the school doesn't. If science or math or reading is important, then you can plan activities accordingly. If the school doesn't do art, then you can do it at home or find outside enrichment classes. As wonderful as the school my kids will go to (starting next year) is, they lack diversity and any sort of perspective on wealth (we will be the poorest by far!) So I am already planning ways to make sure that my children don't think that all the world is white and belongs to the country club. All schools have shortcomings and we have to figure out ways to suppliment what our children learn to make up for them.
Good luck in your search and decision making.