Music in the classical era, typified by Haydn and Mozart, is marked by adherence to sonata form, a way of making tonal (key) contrasts within a composition. Haydn and Mozart were content to follow pre-existing forms such as the symphony,string quartet, concerto, etc.
In the Romantic era, composers such as Berlioz invented new forms almost for every composition they wrote - Berlioz wrote a "Fantastic" symphony, for instance, a symphony which included solos for singers, "Romeo et Juliette". In the Romantic period, the expression of the composer's personal feeling is more important than the form of the music.
Romantic music is also marked by inspiration from literature. Liszt invented a form called "symphonic poems", for instance, trying to put narratives, or stories, into his music as well as the feelings he got from literary works by Dante, Shakespeare, Byron and others.
Larger orchestras and greater musical forces also were used in the Romantic era than in the classical one.
This is a very brief answer on a subject that could have a book written about it.
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Tonic-dominant harmony(apex