In my experience, socialization at school is "broader" in that you meet kids from a wider range of the population, but that breadth is destroyed by the fact that they are all exactly the same age as you are.
Homeschooling brings you into contact with a self-selected subset of the population, but across much wider range of ages.
I split the difference with a Montessori School. Broad range of ages in each class. The whole school interacts during the 2 hour collective lunch and recess time. It's been a good experience for my kid and the school continues in a somewhat similar way after elementary. It's more of home school cooperative than public school in style and I'm okay with that for now. I'd like my daughter to move at her own speed and get more help or more advanced work if she needs it. I just can't be the one to do it. I have no patience
Homeschooling brings you into contact with a self-selected subset of the population, but across much wider range of ages.
This often turns out to be more broadly valuable.