Absolutely it's worth it.
But the real worth of private school comes not in exam grades, nor even in university offers, but rather years down the track in a professional environment when the work ethic, confidence and soft skills instilled by private schools enable their alumni to rise above their state-educated peers.
Academically, I don't think there's much in it between the sectors. A clever kid will do well academically almost anywhere. It's the other stuff - the soft skills, the resilience, and the confidence - that stand to private school kids in the long-term. And in most professions, it's these soft skills - not raw brainpower - that matter most in the long run.
As a friend of mine recently said admiringly of her boys who are now working like Trojans from dawn to dusk in the City, they just find it normal to put the hours in, because that's what school was always like for them. In my region, the average state primary will run from something like 9am to 3.30pm, with some ropey after-school club sketched on for a few more hours of doing not very much. Most of the local Prep schools, in contrast, will run from something like 8.15am to 5.15pm, with further clubs and co-curricular activities scheduled even after that. It's a totally different world. The kids are constantly active and engaged.
If you can afford it, or even semi-afford it, absolutely go for it.
(Caveat: there are, of course, bad private schools and great state schools - I'm talking in the round).