I found that with smaller village schools there tended to be a much higher proportion of SAHMs. Consequently I felt like there wasn't much consideration for working parents, for example mid afternoon events, bake offs, child going up for a special award the next day, with very little notice. I missed a lot of events and ended up feeling like a shit parent, a lot.
There was also no wrap around care and it was a nightmare finding a childminder who'd collect from the school as they preferred to frequent the bigger schools where they could collect multiple children (more clients = more money!), rather than just one or two from the small school.
Much will be personal to the child, so the following is just my experience.
I felt like my son was friends with children because he had to be (lack of choice!) rather than because he had a lot in common with them.
For my son, who is very outgoing and quite loud, I started to notice at around age 7/8 that he was so used to being the Alpha male at school with no questions, that he was struggling to interact with other boys outside of school.
I changed him to a much bigger school (from 96 in the whole small school, to 120 just in his year in the new school!) in year 4 and it was the best thing I've done. His alpha male status is regularly challenged, there's lots of after school clubs and activities, and I know he's friends with certain children because they have lots in common, rather than because they're the only 3 boys in the year group!