It is not true that there is a substantial body of literature that shows that homeschool students do better. The studies that do show this are rife with bias and methodological errors (principally, they tend to design the studies so that most of the children come from higher-income families, who do better in public school too). When you look at more fair samples, the difference isn't so dramatic.
It is very difficult to say whether homeschooling is better or worse academically. The problem is that parents differ dramatically in their teaching ability and their beliefs (some parents' beliefs actively harm their children's educations, e.g. creationism). So it's really really hard to generalize from the studies on homeschool effectiveness to how effective your family will be at promoting academic achievement.
Usually the biggest academic problem areas for homeschool students are math and science, though this may be biased by the large representation of conservative religious groups who homeschool as a matter of faith. Academically, homeschooling may or may not be a benefit depending upon your knowledge and abilities, and upon the quality of your local school system.
It is also worth pointing out that the homeschooling does produce difficulties with socialization. Many homeschool proponents brush off this claim as if it is meaningless, but it really is not. Socialization is about developing a shared social language. It is built from common experiences. Homeschooling children pulls those children out of the path that most people grow up with, which, in turn, means that they are very likely to feel out of place among their peers when they leave homeschool to go to a public school, college, or workforce.
Overall, I'd say it's a decision that has its pros and cons. If you have the ability to homeschool, I would wait and see about the quality of your local school system. If the local school system is of sufficiently high quality, they probably won't do any worse academically if they go to public school, and your child will have an easier time with interacting with their peers later in life.