Mirror Images: Public Option, Charter Schools?

I was struck watching a Lehrer discussion of health care with Ezra Klein and someone else by these thought:

Aren't the arguments for and against charter schools vis a vis public education the same as the arguments for and against the public option and national healthcare?

If I understand correctly, the public ed establishment believed that charter schools would undermines public education through unfair advantages while the supporters thought they would compete with public schools and cause them to improve. (Lots more nuance, I know, but that's the core argument.) Now the supporters of a public option believe it will create competition with private health insurance plans and cause them to improve, while the opponents believe the public plan would have unfair advantages which would undermine the private plans.