A study claims median bills would fall by £279 a year from about £1400 under council tax, the poorest 10% would save £202 but the wealthiest 10% of households would see an increase of £184.
Gross bills would fall by more than 10% for 63% of households, according to the study for the the Joseph Rowntree Foundation by researchers at Heriot-Watt University, but 22.3% would see an increase in their rates.
But the report said a pure property tax would not be fair, and any replacement for the council tax system would need to be related to income.
"At first glance there is a strong case for embedding such a mechanism within the structure of the tax itself, so that it became a hybrid income and property tax," it said.
Council tax in Scotland has been frozen for seven years. The first freeze was part of the concordat agreed by the Scottish Government and local authorities in 2007. However, there have been calls for an end to the freeze amid warnings that local government is "bearing the brunt of cuts".
The SNP had introduced the freeze before the planned introduction of a local income tax. However, that plan was shelved in 2009 amid widespread opposition and claims it was unworkable.
The Heriot-Watt team assessed four different forms of taxation: the existing council tax system, a revalued council tax, a national property taxed based on a fixed percentage of property values and a progressive national property tax based on a higher percentage on the whole of property values over certain thresholds.
Kathleen Kelly, policy and research manager at the Joseph Rowntree Foundation, which is an independent development and social research charity, said any reform of the current council tax system would need to be phased in carefully over time. She also said London would need to be treated as a special case because of its very high property prices.
She said: "Politicians need to start planning for the long-term replacement of council tax. Council tax was a hasty replacement for the hated poll tax 25 years ago.
"It was never designed to last and has not been revalued for more than 20 years: without reform, it will wither and die.
"Freezing bills is a treatment but a long-term cure is needed. This is a difficult reform to carry out, and one that requires courage from all the main political parties. But the problem will not go away and failing to plan for alternatives is storing up trouble for the future."
Professor Chris Leishman, one of the report's authors, said: "Property values have risen substantially since they were last assessed in 1991, but they have grown at different rates between different parts of the country, and even within the same areas.
"The design of the council tax means it taxes a higher proportion from cheaper properties than expensive ones, so is regarded as being both unfair and inconsistent, and certainly in need of long-term reform."
Report co-author Professor Mark Stephens said: "The detailed modelling in this report provides policy makers and politicians with viable, long-term alternatives to the council tax, which is now widely discredited and unpopular.
"All the reforms proposed are revenue neutral. A progressive property tax is one option on offer that could help reduce the burden on households with low to middle incomes, and introduce a fairer system between people and places."