Statistics from the Scottish Council for Independent Schools (Scis) show a slight narrowing of the gap between the two sectors at Higher level.
This year, private schools recorded an overall pass rate of 90.8% compared to 91.3% in 2012, whereas pass rates for all schools have risen from 76.9% to 77.4% over the same period.
For mainstream schools only, the overall pass rate in the independent sector was 93% - the same as last year - while the proportion of exams passed at A grade was 56%.
The pass rate for Advanced Highers was also the same as last year at 92%, with 49% of exams resulting in A grades compared to 50% last year. The best performing school at Higher, according to The Herald's league tables, was George Heriot's, in Edinburgh, with a pass rate of 97.5%. The school, which was founded in 1628, charges £10,299 a year in fees.
Alistair Hector, the school's headmaster, paid tribute to the efforts of pupils and staff for producing its best ever results at Higher.
Mr Hector said extra help for pupils who were struggling in certain areas of the curriculum was key to the success.
He said: "After the preliminary exams we have systems in place which identify where candidates have had a particular difficulty and that allows us to target support in those areas.
"That individualised approach has been a key part of helping all pupils achieve their potential in the last few years."
It was followed closely by two other Edinburgh schools - George Watson's, which recorded a pass rate of 96%, and Mary Erskine, with a pass rate of 95.8%.
In the west of Scotland, there was a difference of only a few percentage points between many of the best known private schools.
St Aloysius' College, Glasgow, came fourth in the league table overall and top in Glasgow with a pass rate of 95.4%.
John Browne, the new headmaster at St Aloysius', said: "I am delighted for the boys and girls. They have achieved academic excellence without losing their many interests outside of the classroom.
"Our young people also show an impressive commitment to serving others outside of the college through many different charitable activities. That they have found time to excel academically is both humbling and inspiring."
The Scis figures also show there was a significant rise in the number of entries at Advanced Higher level, with 187 more candidates than 2012. Of the 22,120 entries nationally, 3572 or 16% were pupils at independent schools.
The Scottish Baccalaureate results showed a 100% pass rate and the number of candidates from the independent sector also rose to 16, representing 9% of the total nationally.
Significantly, Higher French entries at independent schools rose by 12.3% on last year - from 466 to 531 - compared with a decline of 9.6% nationally.
John Edward, director of Scis, said the figures showed the "purposeful learning environment" at Scotland's independent schools.
He said: "Pupils and teachers are to be congratulated for their hard work. At Higher and Advanced Higher level, more than 90% of pupils achieved A-C passes which is a fantastic achievement.
"It is evident that our schools are keeping faith with a breadth of subjects and bucking the national trend, notably in modern languages such as French.
"An important factor in pupils' exam success is that independent schools have the freedom to offer whichever curriculum and qualifications they believe best meet the needs of their pupils, provide breadth and depth of learning and preparation for future studies and work."
Of the schools that study A levels, Merchiston Castle, in Edinburgh, came top with a pass rate of 96.2% followed by Fettes College, also in Edinburgh, with a pass rate of 91.9%.