I'll answer your question by sharing our real-life scenario.
My first son was advanced and we sent him to public school. He wasn't challenged or allowed to advance as much as he was capable. He was bored, but found a love of reading to entertain himself. He's still in public school, and as a seventh grader school work is still very easy for him.
My second son was advanced and we chose to home school him. We didn't want the same thing to happen to him academically.
We also now realize that making geniuses isn't as important as having successful, happy children. We also chose home school for my younger son because he has some challenging behaviors, he has a late summer birthday, and for the values we can teach that public schools don't.
My first son thrives on being social, which is another reason we choose to leave him in public school. My second son is a loner, but we work on socializing in various settings, including church, community, and family functions and in a home school co-op.
I've still very new to home school, but it is so far very rewarding, hard work, and amazing customizing education to your child. I adore all the time we get to spend together!