With private schools you can choose what you pay for (at least in theory), and with public schools you take what you’re given.
Since school education involves lots of contention by different parties over which exact kind of indoctrination and\or mustering and humiliation will the kids experience, I’d say private schools are a good idea in this particular regard.
However, I live in Russia and here both the concept of private schools isn’t quite existent (there are some, but they are very expensive and at the same time not very good, and the prestigious ones are all public, and they’ll have the same standard program anyway) and I haven’t studied in one.
At least somewhere about 9th grade they gave up trying to make me not sleep at all the lessons.