I don't know much about South African private schools to adequately compare them with public or private schools in the United States, but I do have a few recommendations for you to consider.
First, I recommend you get a list of the curriculum from the school your children currently attend in South Africa and compare it with the curriculum of the school(s) you're looking at having them attend in the United States. I would also suggest inquiring about the teaching styles and methods at your children's current school with the American schools you're researching. You will also probably want to compare subject matter and extra-curricular activities, as these could all be important factors to consider for your children.
Meanwhile, here are some national math and science scores for you to review that compare the United States with other countries. Keep in mind that the scores represent a cross-section of the U.S. (students from both public and private institutions) and could differ in the private school arena.
Here are some education.com sites with a host of articles related to choosing the right school for your children. They provide a variety of information on what to look for in a school as you research and visit and whether public or private is a better choice. There are some great, high quality, U.S. public schools out there, so add them to your research list.