The Appassionata is one of Beethoven's most technically and emotionally demanding sonatas. It is defined by its relentless driving energy and explosive structural development.
The performer must maintain extreme finger velocity and rhythmic stability during the piece's most volatile and tempestuous passages.
Comparable difficulty and character — good candidates for what to learn next.
Piano Sonata No. 23 'Appassionata' (Op. 57) is rated Henle level 8 of 9 — concert repertoire, roughly diploma level.
You should be comfortable at Henle level 8 — meaning you can already play level 7–8 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Piano Sonata No. 23 'Appassionata' (Op. 57) lasts about 23 minutes.
Piano Sonata No. 23 'Appassionata' (Op. 57) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 32 Variations in C minor by Ludwig van Beethoven, Piano Sonata No. 21 'Waldstein' by Ludwig van Beethoven, Piano Sonata No. 17 'Tempest', No. 2 by Ludwig van Beethoven — see the full similar-pieces list on this page.