Mrs Rózsa Hoffmann, state secretary (i.e. the highest official specialising in education--her boss, the minister is a specialist in medicine and also responsible for health, sports, social, education and culture issues) for education with a strong catholic background, has already several times emphasised that she intends to improve the situation of faith schools (as well as introduce religious education).
Schools maintained by the local governments receive most of their funds directly from the state budget, but as this is not enough, the local governments have to top these up. For faith schools (and other social services such as homes for the elderly) the situation is a bit different: they not only receive the same state subsidies local government schools, but also the amount the local governments have spent on their schools (in exchange, they have to teach according to hte national curriculum). Of course it's difficult to figure out exactly how much money has been spent by the local governments on their schools, so there is ample room for disagreement and church complaints. This system is enshrined in the Vatican treaty (Concordat) but applied to all faith schools (but not to private schools maintained by others than churches).
Hoffmann now wants to improve the financial situation of faith schools by increasing the ratio of funds provided by the state, saying this should amount to 90% of the costs, and the difference--to be paid by the local governments in the case of local schools--will be taken over by the state in the case of faith schools. From her statement it seems, that though having become a state secretary a few months ago and having been the head of the Pedagogy Department at Pázmány Peter Catholic University (after decades at the ministry of education and as a headmistress of a secondary school), she is not quite familiar with how schools are being financed in the last 12 years. Therefore, contrary to her intentions and somewhat ironically, if this plan is carried out, local governments's secular school will fare better financially compared to the present situation :-).