The findings show that 39 per cent think independent schools have higher standards but 36 per cent believe standards are the same. Nine per cent think standards are higher in the state sector.
Rose Bell of the Independent Schools Information Service said she was "slightly surprised" that the differences were so narrow.
More encouraging news for the independent sector is that 59 per cent of Labour voters say they approve of the assisted places scheme, the lowest percentage of any party. Overall, 65 per cent of Scots back the scheme that Labour is pledged to phase out.
Not unexpectedly, 80 per cent of Conservative voters support the scheme, against 66 per cent of Liberal Democrats and 63 per cent of Scottish Nationalists.