The styles are the antithesis of each other. Obviously, for the Rockschool method, you would focus completely on modern styles of music where ABRSM, for instance, would be completely focussed on classical repertoire.
Generally speaking for the rock stuff you will sing with a backtrack where with the classical stuff you would have piano accompaniment.
According to the official Rockschool Website for a Rockschool exam, you would sing three songs. The first song is chosen from their books, you can also choose a song from the website. Song 1 counts 25 marks and you need 15 marks for a pass.
Song 2, here you can choose another song from the book, you can also choose something of your own composition or some third party piece.
For song two you may add your own accompaniment (Either guitar or keyboard), you are also allowed to be accompanied by another artist. Song 2 counts 25 marks and you need 15 for a pass.
Song 3 you have to choose between one of the two technical focus songs from the book or from the website. They cover three technical aspects of the instrument. It counts 30 marks and you need 18 for a pass.
There is also the session skills that comprise either of playback or improvising. This counts 20 marks and you need 12 for a pass.
SEE MORE HERE.
The ABRSM website gives the following guidance in regards to there voice exams.
Singing exams consist of three accompanied songs at Grades 1–5 and
four accompanied songs at Grades 6–8, chosen by the candidate from the
appropriate lists in the current syllabus, an unaccompanied
traditional song, sight-singing and aural tests.
Total marks in all individual Practical exams are 150. 100 marks are
required to achieve Pass, 120 marks to pass with Merit and 130 marks
to pass with Distinction.
There are eight grades of assessment. Select a grade using the links
below in order to view the syllabus and supporting materials for that