After the passage of the Turnbull government's "Gonski 2.0" funding changes, the focus of the school funding debate is set to shift to state and territory governments and how they respond to the new model.
State governments will have to show "courage" by cutting funding to some schools and redistributing the money to schools in greater need, the Grattan Institute's school program director Peter Goss said.
The Catholic and private school sectors in virtually all states and territories will be over-funded by 2027 unless state governments change the way they fund schools, Grattan Institute modelling shows.
Under the new formula, the federal government will provide 80 per cent of the needs-based funding standard for Catholic and private schools, with state governments expected to make up the remaining 20 per cent.
But state governments currently fund many non-government schools above this level - dramatically so in some cases.
This means some wealthy schools will remain over-funded, despite receiving less funding from Canberra, unless state governments also cut their funding.
Other schools will see their federal funding grow, despite sitting above their needs-based targets.
For example, elite all-girls schools Monte Sant' Angelo Mercy College and Loreto Kirribilli currently receive 80 per cent of their Schooling Resource Standard (SRS) from the NSW government, four times as much as anticipated under the new formula.
Yeshiva College, a private orthodox Jewish school in Bondi, currently receives 130 per cent of its resource standard. But Commonwealth funding for the school will grow strongly in coming years because it is below the new 80 per cent benchmark.
The Victorian government currently funds schools such as Melbourne Grammar School and Methodist Ladies College at 30 per cent of their resource standard, more than anticipated under the new formula.
The situation in Victoria is especially difficult because the Andrews government has enshrined a base funding rate for Catholic and private schools, set at 25 per cent of public school funding, in legislation.
Sixty-five per cent of the country's private schools will be over-funded by 2027, up from 17 per cent now, unless state governments cut funding, according to public school lobby group Save Our Schools.
Mr Goss said: "There will need to be a lot of rebalancing from state governments to ensure all schools reach their targets.
"It will take courage but the precedent has been set.
"Reducing funding for over-funded schools will allow more money to be spent where it will have the most impact."
Mr Goss said the savings would be relatively modest and state governments would still need to find extra money to bring public schools up to the appropriate standard.
NSW public schools are currently funded at 89 per cent of their needs-based standard and Victorian public schools at 83 per cent.
Federal education minister Simon Birmingham said: "Our reforms are a line in the sand for the cost-shifting and blame game that's carried on in the schools funding debate.
"Our Gonski needs-based funding plan means every student will get their fair share of federal support and will apply new levels of transparency to also hold the states to account."
Victorian Education Minister James Merlino said: "We have already introduced legislation that provides a minimum funding allocation for non-government schools.
"We haven't been consulted on Malcolm Turnbull's changes and we are still being drip-fed information about what this actually means for Victorian schools."
NSW Education Minister Rob Stokes said he was examining how to bring all the state's schools to their appropriate funding level.
"NSW will be concerned if the Commonwealth government's funding model has a disproportionate effect on any sector," he said.
"The NSW government supports the right of parents to choose the type of education that best suits their child and is committed to ensuring all students receive a high quality education, no matter what school they attend."