Turning schools into academies does not guarantee that children will get a good education, research suggests.
It argues that there are high levels of variability in standards among academy chains - also known as multi-academy trusts (MATs) and local authorities.
The new study, by the Education Policy Institute (EPI) comes amid a continued push by government for schools to take on academy status, with Education Secretary Nicky Morgan insisting that it is the best way to ensure that youngsters have access to a world-class education.
Researchers compared MATs and local authorities, based on how their schools have improved over time and overall performance, taking into account the starting point of pupils, to create the first ever league table comparing the two types of school group.
The findings show that at primary level, academy chains are over-represented among the best and worst performers in England.
In total, 12 of the top 30 groups are MATs, while 18 are local authorities, while nine of the worst 23 groups are MATs and 14 are councils.
The top performing primary group is the Harris Federation, the report concludes, adding that the improvements it has made is equivalent to pupils making around one-and-a-half terms more progress than average.
At secondary level, six of the top 20 groups are academy chains and the rest are local authorities, while among the worst performing, nine are MATs and 11 are councils.
The Inspiration Trust was found to be the top performing secondary group, with improvements equivalent to students achieving one grade higher in four GCSEs, compared with the average.
"The measures demonstrate the considerable variation in the performance of both multi-academy trusts and local authorities," the report says.
"The variation between different local authorities and between different multi-academy trusts is far greater than the variation between the two groups. This implies that it is more important to ask whether a child is in a high-performing MAT or a high-performing local authority than it is to ask whether a child is in an academy school or a local authority school.
"For example, moving from a school in a high-performing local authority to a school in a low-performing multi-academy trust would appear to risk a significant decline in progress and attainment."
EPI chairman and former education minister David Laws said: "For too long the debate about 'academisation', the possible roles for local authorities in school improvement, and the impact of structural reform on our school system has been dominated by political ideologies, half-truths and hunches, rather than by evidence and careful analysis.
"Governments have seemed unwilling to have a key school reform rigorously tested against the evidence, and too often the critics have also wanted to make their case without reference to the emerging data on how structural change is impacting on attainment and value added.
"Now - for the very first time in our country - it is possible to compare objectively and simply the performance of academy groups and local authorities, in both the primary and secondary phases."
Separate research published today by the Sutton Trust concludes that one in five established academy chains (eight out of 39) are performing below the national average for attainment and improvement among poorer pupils.
The findings, based on the performance of disadvantaged youngsters attending academies in 39 chains between 2013 and 2015, shows that across the sponsored academies in the best chains, the proportion of poorer children gaining five or more good GCSEs is at least 12 percentage points higher than the average for similar pupils in all mainstream schools.