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.