I have the time and money available so home school and private school are options but I also have the option of utilizing some of the best public school systems in the nation. When my first child was approaching school age I had several very candid conversations with people I trust for advice on this particular subject. One of these councilors is a family member that recently retired after a number of years as the Dean of the doctoral education program at a well regarded private university. His years prior to that were spent as a teacher, coach, principal and as a distinguished professor of education in the doctoral program at the same university. His advice was to utilize the public school system in my area. If I weren't in one of the small elite public school systems in the area I suspect his advice may have been different.

Now, with that said, I will admit that the options and tools available to home schoolers have changed significantly since my oldest started school. Home schooling would give my public school option a much better run for it's money today.

IMO any of these options could be the right decision based on the particulars of public and private education in your area and the particular needs and desires of the children involved. I have seen HUGE train wrecks with kids in public, private and home school. The key to all of these is constant, thoughtful parental involvement regardless of which option you choose.
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"There is not a man of us who does not at times need a helping hand to be stretched out to him, and then shame upon him who will not stretch out the helping hand to his brother." -Theodore Roosevelt