Zanzi, the opportunites (not available in all private schools and not unavailable in all state) in no particular order.
1.) Small class sizes. 14 in dd1's and 20 in dd2's
2.) The school goes from 3-18 in a diamond structure with co-ed kindergarten and 6th form and single sex prep and secondary. This means it is a real community. The school really knows the kids. There is a huge amount of communication between the schools so the teachers know exactly what they're getting at transition stages. Having girls I like single-sex (girls thrive academicalyl in single sex where boys do not always) but I also like that the boys are next door and there are lots of co-ed activities e.g. school plays etc so the opposite sex is not considered alien. This means the school can share facilities e.g. swimming pool and library and teaching expertise across the whole school.
3.) Specialist teachers and teaching all the way though the school so the kids have a proper music teacher and proepr language teachers etc from age 4 not just someone who once did French for A Level but actually has a degree in History sort of thing.
Kids have weekly swimming lessons, music, French etc and perhaps this is where there is a more marked differnce than in the average state school.
4.) By definitition all of the parents value education (enough to pay for it or go through the bursary process) which means by and large the kids do too and standards are high. For example, homework is set regularly and it's done by every child. Lots of state schools can't set homework because it won't be done or it benefits the kids from more privilegeed backgrounds and is another stick with which to beat those whose family lives are difficult for one reason or another.
5.) Related to some of the others, a culture which values learning and achievement and respect for others' talents.
6.) Great extra-curricular activiites many in lunchtime so kids get opprotunites to try new things which we wouldn't have time for/energy for in addition to our normal week (whcih does involve 1 extra curricular activity for each hcild).
7.) Great wrap around care: befoer school club, after school club and holiday club run by the same staff so there's continuity, trust, familiarity etc.
8.) I really feel the teachers know my kids and their strenghts and weaknesses. I'm a teacher and hands on parent but the teachers sense when my kids are struggling or ready for the next challenge at about the same time as I do and act on it.
9.) The teachers are not worn down with discipline and workload (because of class sizes etc) so often go the extra mile. DD1's teacher has done some fantastic things with the class in the way of trips and evening activiites etc but really iamginative cross-curricular activiites too.
I could go on.
As I say some of this does go on in state schools but it's not consistent from school to school or year to year.
I also want to repeat that I think all of the above should be available to every child. My kids are not special (except to me) or more deserving just lucky.