Yeah it was also sort of a contest about Italian opera vs. German singspiel (which is like a musical Seraglio and Magic Flute are like this)

It's happening! http://www.pacificoperaproject.com/#!blank/ba1ls

I used to have a recording - on cassette tape, showing my age! - of two short operas, one by each composer, that were originally done as a sort of head-to-head opera-off in the Orangery at the Schnbrunn Palace, with the composers conducting. There were two stages set up, one at each end of the room, so the audience watched the first opera then turned themselves round and watched the second at the other end. Salieri's was
Prima la musica e poi le parole
(First the music, then the words); Mozart's was
Der Schauspieldirektor
(The Impresario).
The sleeve notes said that the audience was asked to vote on the two pieces, and Salieri's won. I can't imagine such an event being staged unless the two composers were on reasonably good terms.
This has nothing whatsoever to do with Shaffer's play/film script, of course, which is a fiction, another variant on his much-worked theme of worthiness versus inspiration -
The Royal Hunt of the Sun, Equus
.