OF course depends on the school and the value of the money to you. Having said that we've moved state to private in yr 2 and are so pleased we did. A lot of the difference is the particular schools but I do think there are pressures on state at the moment that do cause problems. For us the difference is:
Class size. At state there were 30 (with teacher and TA). there may be states like marmitecat's where they can afford to have 20 in a class but not round here. One we saw had 26 but they said they could no longer afford to keep that number and were under LA pressure to take more. In the private there are 12 (with teacher and TA) but several classes of this size that join together through the day for PE/playtime/drama etc so plenty of people to pay with. The class size means atmosphere is very focused and calm. The teacher can see what each child is doing, respond to them and differentiate. DD is bright and was certainly differentiated for in state. They put her up a class for some lessons but as the youngest in the class anyway that didn't work well. In class, the teacher told me that she gave the brightest kids workbooks to get on with whilst she worked with the middle group and the TA had the strugglers. I can understand why but in the private there is not the same pressure on the teacher so it is not such an issue. E.g. DD is a great reader so was read with twice in a whole term at state. Here she reads with a teacher every day. She didn't need help reading the words but her expression, confidence and comprehension have really been encouraged.
The small class size also seems to help behaviour. Our state school had a wealthy catchment so the intake is probably not too different. There were children with significant behavioural difficulties that were not well managed and constantly disrupted the class. The adult ratios clearly made the management of problems harder. There was also a lot of unpleasant behaviour and minor (and major actually) bullying. That's partly a function of the ethos of the school but the adult ratio seems to help as it is much easier at the private to model good behaviour and have zero tolerance of minor things. Teachers sit with them at lunch and there are more there at playtime so problems are dealt with fast.
Resources - the state had quite a lot of playing space and a forest school and they made good use of that. The private has much more space and also has better facilities for art, drama, woodwork etc. They also have specialist teachers in loads of areas. This means the day is much more varied. There is PE three days a week and then gym another and swimming another. Much more art and DT where they are really learning techniques. Loads more drama and public speaking. All this is really helping confidence and enjoyment of school. There are specialist teachers for all these things and for maths, languages, science and english esp in Key stage 2 where they are set.
Testing - the state system seems to have been put under massive target driven stress and that seems to pressure the teachers in ways that aren't always good for the children. E.g. we were told not to worry about DDs virtually illegible writing as the content of her work would get her 3s in her SATs anyway. I couldn't care less what her SATS were, I cared about what she could do! The private is not immune from the pressure of testing but for us it is about entrance exams and scholarships at yr 6 which involve a wide number of different exams so not so much a 'teach to the test' atmosphere. A friend who was a TA in yr 6 at old school said it was just about SATs in yr 6 and nothing else. Actually the private do give them the SATS papers but don't teach it as they are focused on senior entrance. They (non-selective) get almost all level 5.
Attitude to parents - this is not nec the fault of the Head in the state school but the attitude to parents seemed very much that the parents were potential delinquents who couldn't be trusted to make decisions themselves so were sent patronising letters about holidays, attendance, meal provision etc. There was also little feedback save for the structured parents evenings and reports (which I understand given the numbers). Here we get sent home loads of marked work, the teachers are always available and much more responsive.
Sorry for the hugely mammoth post but I think it is right to say it is largely about the particular schools and recognise that many state schools are wonderful. However, I do think that state schools are under huge pressure at the moment with the negative OFSTED regime, targets, pressure on places, funding cuts etc and that easily has an impact in the ways we've seen. The private sector is, of course, not immune from those problems but a well-run, full private is likely to be at a significant advantage.