For myself, it's not the instrument the music is played on, but the music itself. There is no such instrument as a Classical violin, or a Jazz one. The difference is in the music itself, so whichever music one prefers is the determining factor. Classical is mostly formal, "written" music (a Classical violinist plays the notes the composer wrote, not those of the violinists' choosing), Jazz is to a large degree improvised (the violinist plays notes of his own choosing, based on the chord structure of the song). Very different musics.