The biggest impact on a kid's future is their socioeconomic status and/or the determination of their parents. Schooling provided by society is not even a close second, though it does make being a good parent easier (you can delegate 6 or 7 hours a day to society, whereas you'd have to make some really tough decisions if that option wasn't available). We know this is true because social mobility is not that great even in the states; your background matters.

Home schooling tends to just reinforce what is already true about the home environment, so there doesn't seem to be any new variable their. Of course, we could argue that schools can have adverse effects and that you are avoiding those by homeschooling, but since home life is so dominant, you'd expect kids to just regurjitate what they've learned at home anyways, at least until middle or high school where teenagers begin to break free.