That aside, this is a pretty obvious attempt to defund the Catholic school system. If outcomes truly are simliar between the systems why are they moving funding away from the Catholic system?
For the past thirty years, the private education sector has been heavily subsidised by the federal government. The idea was to make private education accessible and affordable to everyone. It worked, but the system is out-dated - the schools still get paid, but under the terms of the original deal, which uses economic data from thirty years ago. Since the average family is better off now than they were then, the government is paying a massive subsidy.
The new model is needs-based funding. Individual schools get paid based on their performance with under-achieving schools getting more money. This applies to every school, not just the public ones, and the money is paid directly to them. Under the current system, the money is paid to the diocese, who distribute it to their schools as they see fit. This has led to the suggestion that diocese are giving their funding to the best-performing schools, although I haven't seen any convincing data to go with it. The individual schools offering the most resistance are the ones in regions where educational outcomes are low; they won't so much lose money as see the state schools get more funding, but because they're a business they'll still be better off.
Don't get me wrong, the Catholic system is very good. They're run as a business first, and they're extraordinarily well-off. If a new school is being built, chances are it's a Catholic school, and in some towns they have a virtual monopoly on education. But they're a lot like Ferrari - they get paid simply for showing up, and now they're complaining that the gravy train is making a few more stops along the line.
I do have issues with the proposed funding model. Needs-based funding is the way to go, but this system is a cheap imitation of the previous proposal. The current government scuppered the proposal when in opposition, but now that they're in government they've revived it, watered it down and are now pretending it is something new.