I think it's worth the money, definitely - or at least the ones I went to were worth it.
In terms of academics, it's certainly possible to do just as well at a state school. But I think attending a private school makes you more likely to really want to do well for yourself. You're in an environment in which academic achievements are considered to be very respectable (e.g. rather than something you're teased or bullied for), and in which most other people are very successful, which sets the competitive bar very high. It adds to a pupil's desire to succeed and gives them the confidence that they can. People can genuinely aspire to study the most competitive degrees at the top universities, because instead of thinking "that's just for Aspergic nerds, not for me", they think "well, all my friends are going so why shouldn't I?"
Also, school and life in general aren't just about academics. I think the private schools I went to were great at giving us lots of opportunities to broaden our education and life experiences beyond just being exam machines. For example, rather than just visiting a local church, one Religious Studies trip was to the Vatican itself. Rather than just playing a Rugby match against the local rival school, the team travelled to Australia and New Zealand to compete against teams there. Members of the orchestras and drama societies have the opportunity from a young age, to regularly perform at venues such as the Symphony Hall in front of very large audience, so it's little surprise that they have no nerves when doing it at an older age. The school provides a vast array of facilities, activities and additional training to help the child reach their full potential in whatever their own personal area of interest might be; sports, music, drama, travel, arts, leadership and teamwork, public speaking or debating, programming, chess, you name it. It provides them with a really broad education, the opportunity to pursue whatever activity the they might thrive in, and the confidence to think that nothing is beyond them or out of their reach. Even if a pupil said "I want to be the Prime Minister when I'm older," he wouldn't be laughed at for living in a ridiculous dream world, he'd be told "okay, do it then".
Having said that, it's up to the child to make full use of what is being made available to them. If they are the type of kid who literally just goes to school, sits in lessons, comes home and then gets average grades, then no it's probably not worth it because you can do that at any school. It's worth it for those who immerse themselves in everything the school has to offer.