I have been in public school and I went through homeschool before recently graduating so this might help.
Pros of homeschool are: You graduate way faster, You have more freedom in your school decisions, you chose your amount of work, and you typically do it whenever you'd like. Cons of homeschool are: You get extremely lonely, you get bored a lot more often, you lose friends, and you can become lazy.
Pros of public school: You have teachers to teach you different ways, you are more social, you have more friends to help you out and school is typically easier. Cons of public school are: There is way more drama, especially in high school. You have more options to be lazier. You have less work, and you are influenced by many of the people you are around.
Some upsides to home schooling would be that you can focus more on what you want to learn. With public schooling you are gonna have to learn what the teacher is putting out that day . Another upside would be that you can learn at your on level and time, with public schooling you have to stay with everyone on everyone's level. Some downsides would be that you don't get to interact with your friends or teachers everyday. Another would be that you might not have the same social skills as one that went to public school
