DrCoconut as previously stated, the suitability of any school can only be ascertained by a visit to the school and clear understanding of what you want to get out of it.
Swapping between state and private will undoubtedly bring about complications due to the fact that they may follow a different curriculum.
Regarding the social differences, I think people often have the impression that all private schools are like Eton. I'm sure some are. However, given that some are now being used for streaming into Grammar, super selectives, semi-selectives etc., in this instance, there would likely be a very diverse cultural range. After all, you don't need to be rich or a snob to be academically focused.
Additionally, in areas where school places are in short supply and parents are not getting any of their preferences, private schools are often considered as the fall back option. This too is likely to result in a diverse cultural range.
Some people believe that private schools get much better results than state schools. However, some private schools achieve pretty mediocre or even dire GCSE and A level results as do some state schools.
To be honest, Im not sure getting a general insight into the pros and cons of state vs private is really going to help you decide what is best for your DCs.
Perhaps if you short listed the various schools you are currently considering, and perhaps ask for opinions on those specific schools, you may get the answers your are looking for.