My youngest is at nursery in the pre-prep dept of a prep school 20 mins away (which we chose as it was a small setting and we really liked the staff who were gentle and "got" preschooler and toddlers). He will join his sister at our very small local state primary in September.
The prep has lovely facilities and grounds, the music is better and there is much more space and a great variety of activities (ponies, mountain biking, rugby, tennis, archery, they have their own pool etc etc etc).
The state primary is a small building - really they need an additional classroom or two, and while there is a playground and a little garden, there is not field after field of space like there is at the prep. Inside space is used to the max. Class sizes are however small because it is a small school (average probably 7/8 in each year - often two year groups are taught together).
The extra curricular stuff is not bad at the state primary, they do a couple of really quite impressive theatre/musical productions each year, and lots of adventure things like camping, building rafts, camping out and making pizzas on a fire, forest schools, swimming every week for the whole school, PE and gym at the local secondary each week, dance and so on. However there are no sports pitches so there is no tennis/rugby/hockey etc. Music is ok - they sing a lot - but there is no orchestra/band and although there are grouped violin and guitar lessons the kids seem to progress quite slowly (whereas at the prep they do concerts when each kid does a solo and they progress much faster with a dedicated music department there).
However the state primary is "our school" - part of our community here. Many walk to school, the kids know all the mums and dads and where all their fellow pupils live. You would never get that feeling with the prep (kids are driven/bussed in from a wide area). I think that is really important - little children love to feel connected at school and ours is like one big family for them. It is also a very kind, small school with practically no bullying, and where older and younger children mix together. The values are strong around kindness, inclusiveness, trying your best and so on. The head is very inspiring and really lives to help our school be even better than it currently is.
I don't think the prep is any better academically. My eldest is well above expectations academically and they differentiate so that they are getting appropriate work, mine is doing Y3/4 work now as a Y2. Bright children are entered for level 5 and 6 SATS. There is also very careful monitoring and intervention for any child who is finding any particular thing tricky.
I don't think its "state v private" - it's more do I prefer THIS PARTICULAR private school over this particular state school? They are all different. The state schools around us are some of them quite different in character to ours!