There are a number of great answers already, which provide a good balance of views, and show advantages on both sides of the question. However, generally speaking, these answers are anecdotal, and do not provide a holistic view of homeschooling versus traditional schooling.
First, a word of caution. I have extensively reviewed the research, and find people who conduct this research seem to have a built-in bias toward homeschooling (they either already have a homeschooling background, or are sponsored by an organization that supports homeschooling).
A survey of research papers on the comparison of test results between home-schooled and traditionally-schooled students are pretty conclusive and indicate that home-schooled students do get better results. Depending on the source, the answers range from “somewhat better” to “scored in the 86th to 92nd percent statistically”. “NHERI found that 13,549 homeschool seniors participated in the 2014 SAT. Of those seniors, homeschoolers scored an average of 567 in critical reading, 521 in mathematics, and 535 in writing. In comparison, the average SAT scores for all 2014 high school seniors were 497 in critical reading, 513 in mathematics, and 487 in writing.”
One interesting article by Gwen Dewar cites a Canadian study, indicating that homeschooled students in a structured curriculum did significantly better than traditionally-schooled students, while those in an unstructured homeschool environment did significantly worse.
“In 5 of 7 test areas, (word identification, phonic decoding, science, social science, humanities) structured homeschoolers were at least one grade level ahead of public schoolers.
They were almost half a year ahead in math, and slightly, but not significantly, advanced in reading comprehension.”
“Researchers calculated the probabilities of getting these results due to random chance alone. For science and calculation, these probabilities were 1.9% and 2.6%. For word identification, decoding, and social science, the probabilities were all below 0.07%.”
“In every test area, unstructured homeschoolers got lower scores than the structured homeschoolers did.
In 5 of 7 areas, the differences were substantial, ranging from 1.32 grade levels for the math test to 4.2 grade levels for the word identification test.
Where the structured homeschoolers performed above grade level, the unstructured homeschoolers performed below it.
The chance that unstructured homeschoolers performed worse due to random factors? Less than 0.07%.”
– See more at: Homeschooling outcomes: How do they compare?
What does it all mean?
It is important to recognize that each homeschooling experience is different, and will produce different outcomes. (This is also one of the most important reasons for homeschooling – since each child is different, and will learn differently).
The results of a homeschool education will only be as good as the planning, effort, and curricular choices made by the students and teachers (in this case, usually the family).