The Education Policy Institute think tank has produced a league table of academy trusts and councils in England.
David Laws, former schools minister and the institute's chairman, said successive governments had been "in denial" about failing academies.
The Local Government Association said it showed academies were no "magic bullet" for improving schools.
A Department for Education spokesman said: "Our ambition remains for all schools to become academies."
Mr Laws said that when he served as education minister in the coalition government there had been internal data showing weaknesses in academy trusts, but there had been a reluctance to publish such information when ministers were promoting academy expansion.
But the Education Policy Institute has now published its own rankings showing how local authorities compare with multi-academy trusts with at least five schools.
The findings show that academy trusts are among the most and least successful at improving pupil performance, at both primary and secondary level.
In between is a spread of success and underachievement, with the analysis concluding that there is little overall difference between academy trusts and local authorities.
The average for academy trusts and local authorities is described as "almost identical".
Mr Laws says that it shows it would have been "rash and dangerous" to press ahead with forcing all schools to become academies, as it would have meant that some high-achieving local authorities could have been put into lower-achieving academy trusts.
The former education minister said that for successive governments there had been a "lack of political will to show that some academies are not doing well".
Mr Laws, a former Liberal Democrat MP, said that a "lot of political capital has been invested" in presenting academies as the way to raise school standards.
Education Secretary Nicky Morgan has had to abandon plans to force all schools to become academies, but Mr Laws says their political protection went back to the early days of the first academies created by Labour governments.
Mr Laws said that they were seen by the government as "a small and precious flower that people wanted to stamp on".
The comparisons produced by the think tank are based on how much pupils have improved, rather than exam results, as a way of measuring the effectiveness of local authorities and academy trusts.
Many academies operate as stand-alone schools, so these are not included in the rankings, which compare multi-academy trusts.
Mr Laws said that the findings highlighted the need to find ways to scrutinise and improve weak academy chains - but that did not mean that the principle of academies, with greater autonomy, was flawed.
But he suggested that it showed successful local authorities should be able to set up their own academy trusts, rather than have schools taken away from them.
Report author Jon Andrews also highlighted other factors, such as regional differences. Schools in London are higher performers - and he says that both local authorities and academy trusts are likely to do better if they have schools in the capital.
The Sutton Trust education charity has also published a report warning that too many academy trusts are not providing a good enough education for disadvantaged pupils.
It says that one in five academy chains is "performing substantially below the national average for attainment and improvement" for children from poorer families.
Lizzie Rowe, chief operating officer of the Education Fellowship, the lowest rated primary academy trust, said that trusts needed to be given time to make progress and that this was not always shown in immediate results.
"Data enables you to judge the pace and direction of a journey - data is not the journey. Some political powers forget this.
"Our strategy is very sound in developing leadership and enabling teachers to deliver outstanding lessons.
"Some of the most successful academies started well over a decade ago and were given millions of pounds to get established. We are a new trust working within an area of neglect and deprivation by all political bodies."
She said: "We receive no support from our regional schools commissioner, only negative challenge."
Roy Perry, chairman of the Local Government Association's children and young people board, said: "Councils have long been highlighting the fact that school structures are not a magic bullet to improve education, and what really matters is outstanding teaching and strong leadership.
"Every school and every community is different, and head teachers need the freedom to choose, in partnership with parents and councils, the structure that is most appropriate for them."
A Department for Education spokesman said: "These reports highlight many impressive multi-academy trusts that are driving up standards and delivering an excellent education to thousands of children across the country.
"They are playing a vital and increasingly important role in the school system - thanks to their ability to share resources, expertise and provide support to schools that are struggling.
"Our ambition remains for all schools to become academies with more schools joining multi-academy trusts - our evidence shows this is the best way to bring about sustained improvement."
Top performing secondary academy trusts and local authorities, based on pupil improvement
1. Inspiration
2. Barnet
3. Merton
4. Southwark
5. Outwood Grange
6. Hackney
7. Kent Catholic Schools Partnership
8. Wokingham
9. Surrey
10. Peterborough
Lowest performing secondary academy trusts and local authorities
165. Salford
166. Stoke on Trent
167. Newcastle upon Tyne
168. Woodard
169. Wolverhampton
170. Greenwood
171. Oldham
172. Nottingham
173. Knowsley
174. College Academies Trust
Top performing primary academy trusts and local authorities, based on pupil improvement
1. Harris Federation
2. First Federation Trust
3. Redcar and Cleveland
4. Kensington and Chelsea
5. Greenwich
= Camden
= Newham
= CFBT Schools Trust
Hounslow
Waltham Forest
Darlington
LEAD
Reach2
Lowest performing primary academy trusts and local authorities, based on pupil improvement
212. Discovery
= Walsall
= Diocese of Leicester
= Diocese of Norwich
216. Rutland
217. Poole
218. Education Fellowship Trust
Academy trusts are no better than local authorities at raising school standards, researchers have found.