The Turnbull Government plans to inject $19 billion into schools over the next decade.
Over 9,000 schools would benefit, while just 24 private schools would lose money.
A further 350 schools would receive a funding boost, but less money than they were expecting under previous deals.
And the Catholic education sector is complaining many of its schools would lose out after what it has said is a lack of consultation.
The director of Catholic Education in Canberra, Ross Fox, says it could affect schools' fees.
"Yesterday, the Minister and the Prime Minister announced a plan that will see pressure on Catholic school fees and, therefore, will reduce the choice that parents have in choosing a school for their kids."
Education Minister Simon Birmingham has rejected that criticism, saying Catholic schools would be funded the same way as any other private school under the plan.
"Unsurprisingly, people who didn't get everything they asked for might sometimes complain about the consultation. That doesn't mean there wasn't consultation. It just means that we are not going to continue with a system that is based on special deals for one state or another state, one sector or another sector. Our proposal is to treat every school fairly, equitably, under the same terms, regardless of their background, regardless of their school sector, regardless of their faith."
In the next four years, non-government schools would get a funding increase of $1.2 billion, while government schools would get $2.2 billion.
But Labor is accusing the Government of actually cutting funds from education, because the total amount is less than what Labor promised when it was in power.
Deputy Opposition Leader Tanya Plibersek says the Government is using the name of David Gonski, who led the committee behind Labor's plan, to sell a worse deal now.
Mr Gonski has stood with Prime Minister Malcolm Turnbull on the new plan, but she says the reality about the plan remains.
"This education funding cut announcement is the new Coke of education announcements. This is taking a trusted brand and using that to cover up an inferior product, a product that no Australian parent will buy."
The Greens say they want to see more details but are cautiously supporting the changes.
Greens leader Richard di Natale has welcomed the funding cut for some wealthy private schools on the east coast.
"If that means making sure that a tennis court doesn't get built, or an extra swimming pool doesn't get built, or another set of rowing sheds doesn't get built in a wealthy private school, so that our public schools get the facilities and infrastructure that they need to give kids the best start in life, well, we'll do that."
But there was less enthusiasm from the Government's state Liberal colleagues in New South Wales.
The state's education minister, Rob Stokes, has threatened court action to protect the funding the state negotiated with the previous Labor Government.
Premier Gladys Berejiklian says her Government is not backing down.
"New South Wales doesn't shy away from the fact that we expect the original agreements and funding arrangements we signed up to to be delivered. And that's a position we'll continue to advocate. So we were very pleased to be the first state to sign up to the Gonski agreements, and we will continue to ensure those agreements are honoured. And, we've articulated that publicly and privately to our colleagues over a number of occasions and will continue to do that, and that's something we won't digress from."
