Is homeschooling better than public school?
Depends what you expect your kid to learn while it goes to school.
If you expect it to learn to get along with others who aren't in your family. definitly.
For the classes itself it depends, are you able to teach your kids as well as soneone who learned it. That for one requires that you are as knowledgeable as all the teachers your kid would have in school together. Are you able to find a pedagogic style that really fits your kid. That sounds easier than it is, especialy if it's your own kid. Your own expectations might fool you here.
I'm not a big fan of homeschooling as the most doing it din't really know how to do it well. And I apreciate that here (in Austria) if you do homeschooling the kids need to take exams on schools as that guarantees at least a minimum level of stuff learned.
There are situations where I would recommend it, but that is rather if the situation on a school drags a kid too mich down (e.g. mobbing) and the school staff is nit able to stop that. But as a general way of teaching kids there are too less parents that realy have the competencies to teach well.