I remember both taking off in parallel with very different support basis; the movement for privately operated charter schools has taken off when and where vouchers-for-private-schools haven't succeeded, but the publicly-operated charters that function as alternative-model public schools still exist and are still something that reformers that aren't supporters of the education privatization movement push (and sometimes nearby areas -- possibly even the same districts -- will have both kinds of charters.)
> There's a lot of isomorphic economic policy between the two, although if I had to pick I'd say charters are better than vouchers.
Between vouchers and privately-operated charters, I don't think you can make a useful of which is better; it mostly comes down to conditions, management, and accountability measures; charters probably make it administratively simpler to avoid the worst problems, but also tend to be greater single-point-of-failure systems.
That depends; there are lots of different kinds of charters. Charters are public schools that have some exceptions -- enshrined in a particular charter, hence the name -- to the generally-applicable rules for public schools in the jurisdiction. These can be exception in terms of administrative process, specialty curriculum, alternate non-geographic admission criteria, etc.
They can also be exceptions in that the whole operation of the school is contracted out to a private entity, making it essentially a private school where tuition is entirely publicly paid for a cherry-picked student population with less accountability to the public than is usually the case with public schools. But that's not always the case.