State ed and in fact the vast majority of independent ed, has never offered the intellectual breadth of education my DS school offers. It's what my DS's school is known for. On the other hand it doesn't offer things that other big name schools do offer.
I don't dispute that your DS's school may offer something unique and unusual, so perhaps it is indeed worth paying for. I'm obviously unfamiliar with the offerings of all private schools, so I am basing my comments on the ones that I do know something about. These include many of the less known independent schools as well as some of the more famous schools such as Wycombe Abbey, St Paul's, Eton, Winchester, Cheltenham Ladies College and so on. Having known many people that went to these schools (and others who send their dc to these schools), I am not at all persuaded that they had a broader or better education than myself.
The only real difference that I did detect with regard to pupils who had attended certain schools was perhaps an ability to talk confidently about subjects that they didn't really understand. I think this relates to the veneer of confidence that I mentioned earlier on, and I did admire it when I was around 18, but it's all fairly superficial stuff in my view. I guess it can be a useful skill to have at times, as it may impress or intimidate people who aren't able to see through it, but it's not something I would value, and personally, I'd prefer schools to encourage intellectual honesty and the courage to admit when you don't really understand. Again, I'm sure many indie schools do this, I'm just talking about the ones I happen to know.
As for secondary schools teaching to the test, I think this can go on in both sectors, but it doesn't necessarily happen to the same degree in all schools. When dd gets to secondary age, we will obviously evaluate all options and make the best choice. We may well have to move to get what we want in any case, as neither sector offers what we want locally, and I would not be prepared to consider boarding.