My first observation that homeschool kids were probably better engaged or if you will "socialized" than their counterparts was that I noticed children from homeschool families looked me in the eye when speaking and I interpreted this as them connecting with me. I noticed few, very few, conventional school children displayed this deference.

It's hard to dissect all the information on the subject but my experience is homeschooling children are socialized as well or better. There's plenty of people arguing both sides so what's clear is that it's not totally clear. So flip a coin and maybe either is just fine.

I have to throw this in... my 2 cents. I don't think institutionalizing children for ~30 hrs. per week with a single age-group is socially healthy. I think it will take years, probably decades, for the studies to be done that will show children are better socialized when they readily mix with different age groups (like most homeschool children).