In other words is it simply a case of $10 000 per child per year, so here's a voucher for 10k, go wherever you like?
There are no extra resources here for underperforming schools - in fact there are likely fewer resources. Public shools won't get smaller though, they'll just merge together to create fewer schools, and the bad teachers will go away.
And perhaps therein lies the root of the resistance to vouchers. It starts to measure school, and by extension, teacher quality. And that's not a rabbit hole teacher unions want to go down.
When vouchers were proposed in California in 1993, it was to be half the amount spent by the state on each child for public education. In 2000, it was to be $4000/year, when the state spent about $7000/year per student.
Of course, there's the big existing population in private schools that would also have been eligible for vouchers-- about 7%-- so these amounts probably still would drive down per-pupil spending in public schools. You'd need to roughly double private school enrollment to "break even" in per-pupil spending.
I favor something like 20-33%-- that might reasonably be expected to both make it significantly easier for parents to send their children to private schools and increase resources per student in public schools.
Of course, it still takes thought to make sure that the public schools improve in this scenario, because they will also be fighting an adverse-selection headwind of being stuck with students from lower classes and those that the private schools don't want. But if you can shrink classes and cater classes to similar ability levels, I'd think this would win out.