I have had both my DDs at private and state schools. Way too many infact but thats because of our mobile lifestyle (Forces).
Eldest DD went private in reception. My youngest DD went to a fab state school in reception.
Both DDs could read when they started school.
Eldest DD (private) started straight into full school days and brought home books suited to her level of reading and she progressed quickly through the reading programme. By Xmas there was a marked and very obvious improvement in her reading skills.
Youngest DD (state) started on a part time system and it was the every end of Spetember before she did a full school day. Despite being able to read she was sent home with picture books. I went into school and explained she could read but was told ALL reception children start at the same level so any less able children have time to catch up. I was told reception was not really about academics but more about learning social skills and that proper academic work would start in year 1.
I have to say although frustrated with this attitude the teacher was lovely, felt her career choice was more a vocation iykwim, she was so caring with the little ones and the school had a wonderful atmosphere in general. It was lovely to walk to school and be in our village. However even DD2 was getting bored with her picture books and tbh - we rarely sat down to look at them as it all seemed pointless. Luckily eldest DD had some old books which DD2 would read. By the Xmas - DD2 was holding her own but there was no real improvement in her reading. Had we not been posted and moved house. I do think we may have considerd moving DD2 into privte school by year 1.
This is one example of just 2 different schools. All State and Privte schools are different. You get good and bad in both. There are pros and cons to both types of schools and really only YOU can decide what you think will be best for your DD.
Both my DDs have moved in and out of both state and private schools and pre year 4 its easy to do. I only say year 4 because in my DDs current prep school this is the year when ALL subjects are taught by specialist teachers and they move around the campus to different lessons. IE: Science in a lab, French in a language classroom/lab. etc etc. I dont know if either would now find sitting in one classroom with 1 main teacher all day a bit boring now - only because of what they have become familiar with. Pre year 4 most subjects are taught by their main teacher with maybe just someone in for Art, French, Music etc. So not too different to any state primary.
Its an agonising decision. I am pro whatever suits anyone and their kids at the time and hate the assumption (some people make) because my kids are currently in prep school I am a toff or anti state schools! That is something to be aware of - if you go private. Some people seem to take it s a personal snub to them and also seem to think they have the right to comment on your choice!
My DDs now board (another emotive topic)and to me the biggest downside (atm) to their private schooling is I feel they are leading a blinkerd existnce with ALOT of very privelidged kids from very wealthy backgrounds. Not all are like this - there is mix of people who sacrafice hell of alot to pay for it, Forces families like us etc. as well but tbh - there are no real poverty cases at the school and I do worry about the fact my girls are in this "bubble". Not such a worry for day children, as they can still mix with the broader and local community through Brownies, Gym clubs etc.
Sorry for the long post. But hope some of my insight may help you little.