Schools in Wales rated their local authorities' services more positively than those in England.
The survey of 8,000 schools across 150 local education authorities in England and Wales was carried out by public-spending watchdog, the Audit Commission; Estyn, the schools inspectorate and, its English counterpart, the Office for Standards in Education.
Conwy was the best-performing Welsh authority while the Vale of Glamorgan was the least praised.
Overall, results show a wide variation in the quality of services in different areas.
Primary schools are more likely than secondaries to praise their LEA.
Schools were least satisfied with the support offered for special needs pupils.
Complaints about access to management support services and the quality of building maintenance were also common.
Hartlepool and Conwy were both ranked in the top 10 authorities for more than 50 of the 76 questions asked. However, 19 authorities, including the Vale of Glamorgan, Liverpool and Norfolk did not achieve any top 10 placings.
Sixty-five LEAs, including seven in Wales, were excluded from this analysis because fewer than 38 per cent of their schools responded.
In England, schools in shire authorities and in inner London are most satisfied with council services. Schools in the capital were particularly happy with support for teacher recruitment and raising attainment at key stage 3.
Outer London authorities were rated most negatively by their schools with support for 14-19 education seen as particularly weak.
A spokesman from Conwy said the council's success was based on a strong partnership between school staff and LEA officers.
He said: "A powerful, challenging and open relationship exists between everyone who works in the service in Conwy to continually improve standards."