The YouGov study found 62% of those questioned in Scotland preferred council-run schools - the highest figure in the UK.
London had the highest proportion backing private education, with 35% saying they would send children to comprehensive schools if money was not an issue.
Those would prefer a private education said they thought their children would be less likely to be bullied in an independent school.
They also thought private schools offered a better education, had superior teachers and offered better networking opportunities.
Those parents with children already at private school said they were spending an average of £15,000, but some were struggling to meet the fees on their own.
One-quarter are relying on grandparents to help out, while one in ten are using pensions to pay for the schools.
Meanwhile, those who backed the state sector said they believed their children would benefit from mixing with pupils from all walks of life.
Richard Boyd, chartered financial planner at Duncan Lawrie Private Bank, which commissioned the survey said: "Choosing which school you send your children to is more than just about money - parents understandably want the best for their children.
"The choice parents make over schools is predominantly based on perception of what they believe the school can offer their child growing up."