Having had children go through both sectors the advantages of a prep school for me are 3 things.
A) a more thorough grounding in the basics such as spelling, handwriting, accurate grammar, learning times tables by rote. Ok isn't good enough, if work is sloppy it has to be done again and as a result my children have a real pride in their work. The overall teaching is better, the lessons are modern and progressive combined with tradition. It's a far better grounding in my experience. I'm sure there are state schools who do similar but the good with outstanding features my older ones were at certainly didn't.
B) breadth of opportunities, even in a reasonably small but not tiny prep these are huge. My DC are doing huge amounts of sport, music, drama that they could only dream of in their state school. Again, this can all be done out of school but it adds to the overall experience.
C) Communication. This for me is key. Again, perhaps it's common in state schools but not in my experience. I have the teachers email address. If I need to contact them they respond immediately. If there is an issue there is no brushing it under the carpet. DC will come home and tell me something has happened and by the time I speak to the teacher it's dealt with, an action plan has been put in place and I am kept informed at all stages.
The school may not be teaching 3 years ahead for all children, it's non selective so there are children of all abilities but my DC are certainly ahead of the state school friends and that gap does become more evident by years 4/5/6 where even the average attainers are miles ahead of the top children at the previous state school but at pre-prep level it's less obvious and the school doesn't prepare at all for 7+.
I haven't come across any spoilt or entitled children, many of them are from extremely affluent families but they are generally absolutely delightful children.