Over here in Netherlands they don't have this public and private divide. It's hard to explain (and I'm not totally sure if I understand it right, and it is only my experience with primary schools).
All the schools receive funding from the government based upon their enrolment. Apart from meeting certain benchmarks, the schools are completely independent. They can set their own hours (we currently have 4 days a week), their own teaching philosophy and anything else!
There is a 'voluntary' contribution for extra stuff like excursions or music or things like that. Ours is on the expensive side of things (500 euro per year, or 300 for low income), but it really isn't compared to what school fees could be.
The system has its advantages and disadvantages (like all systems), but on the whole it seems to work okay.
I wish we have that system here too.....
Schools should not be judged because it is a public school or private school but with the school's and teacher's performance.
There are also less good things about this system as well.
Most people don't travel more than about 5 or 10 minutes walk or bike to their school (we unusually travel about 25 minutes by car). So it tends to be that the better schools tend to be concentrated in richer areas. So, the better teachers want to go to those schools, so those schools do better... Endless cycle!
And, coming from the Australian system, the huge variety of teaching methods is absolutely bewildering! Who knew there were so many ways to teach kids!