I moved my DD, yr1 to a prep school earlier this year leaving DS at the state school.
To be perfectly honest, I don't see enormous differences but the state school is an extremely middle class school with an almost identical profile to the prep school.
There is more uniform and i constantly have to remember what she needs to take on which day. She takes sports kit in 4 times a week where as DS only takes 3 times a week.
Whilst the private uniform is more expensive they are less fussy than I had expected, the regulation skirt is, in most cases substituted with the M&S version and most of the girls are wearing Sainsbury / Tesco's version of the summer dress.
There is far LESS involvement from the parents in the private school. She has a speech day at the end of the month, a sports day, and a summer fair. These are the first things I have been asked to attend since she started. DS has all of the above plus other assemblies, parents forum, curriculum meetings and all sorts. State school thinks nothing of holding compulsory meetings at 3.30 in the afternoon, private school manages to do all this via letter or email.
DD has the options of the same music lessons as DS. Neither are musical or learn instruments and there is no expectation that they take them up.
Pressure to socialise and to micro-manage their children's social life is far less in the private school, most parents are dropping off and running to work. In the state school there are far too many SAHM's with too much time on their hands.
Outings are broadly similar, DS has had 2 outings this year, one was £13, the other £40!
DD has had 3 outings, one for £13, one for £14 and one for £24
The key thing I have noticed is the emphasis on core skills is much higher in the private school. My DD has accelerated her learning particularly in relation to handwriting, spelling and punctuation and her teacher has much higher demands in this respect than her teachers in the state school. However, DS in yr4 has homework every night, maths, literacy, science, humanities plus a library book each week. I think that the private school will be similar by the same point.
The smaller class size has made the biggest difference. DD is very shy and insecure and her teacher knows all the children very very well in a way that only the best and most experienced teachers at the state school could. She is getting far more one to one in her new class than she ever did in the old class. As a child who sits in the middle of the class this is the biggest benefit. DS has always been one of the top performers and wouldn't have seen the same benefits.
As she gets older there will be more emphasis on sports in the private school and she may have the opportunity to play more matches. DS has played about 5 matches all year but we top that up with out of school sport, I think that DS will have residential trips in yr 5 & 6 where as DD will have in yr 4,5&6.
I think that it completely depends what you are coming from and going to in terms of schools. My friends and I often joke that the state school is suffering an identity crisis and thinks that it is is private school the way that it behaves hence why I think that I haven't found huge differences.