The Scottish sample of 906 found that 53% of respondents viewed Nicola Sturgeon’s performance above the rating of 50 out of 100, giving the SNP leader an +11% net approval rating.
The poll by Tory peer Lord Ashcroft found 54% of respondents north of the border placed Ruth Davidson below 50 out of 100, with 58% having a similar view of Theresa May’s performance.
Respondents were asked to rate politicians from one-100, with zero meaning “terrible” and 100 equalling “excellent”.
Scottish Labour leader Kezia Dugdale had a net approval rating of -41%, with 20% of respondents rating her above 50 and a further 61% placing her below the half way point.
But respondents UK-wide took a more favourable view of Davidson’s performance, with a mean score of 38.1. The First Minister scored 32.4.
Meanwhile, 55% of 10,000 respondents UK-wide said Theresa May would make the best Prime Minister, with just 18% backing Jeremy Corbyn.
May had a 37-point lead over Jeremy Corbyn on the question of who would make the best Prime Minister.
While nine out of ten Conservative voters chose May, only 38 per cent of 2015 Labour voters named Corbyn. Those who had voted Labour in at the election and Leave in the EU referendum preferred Theresa May by 40 per cent to 30 per cent.