I am afraid Beethoven did not write preludes.
A very interesting comparison of preludes would be J. S. Bach, Chopin, Debussy, Shostakovitch (op. 87 rather than op. 34), and Rachmaninoff, since the composers themselves (Bach excepted of course) acknowledged links. It has of course been done before.
Sonata form again is a promising form, since you can trace its evolution through all periods of music.
Another interesting form is the dance suite (e.g. Baroque: Handel suites and Bach’s partitas – Romantic: Grieg’s Holberg Suite – Impressionist: Debussy’s Suite Bergamasque & Suite pour le Piano – Ravel’s Le Tombeau de Couperin - Modern: Rakov’s Classical Suite)
Fantasias and Impromptus are again another interesting form (formless?) that can be found in all musical periods.
Best wishes,
Bernhard.