What features of the earlier piano sonata might lead you to describe this as a Classical piece?
The earlier sonata conforms to the four-movement sonata form which became prevalent toward the end of the classical period after taking Beethoven’s lead.
Does the later work retain any of these Classical elements?
The earlier, classical sonata form under Beethoven’s influence moved from a three movement Allegro-Adagio-Presto (fast-slow-fast) format to a more malleable arrangement where the tempi or presentations of the work could be moved. Although this change provided composers with greater scope to rearrange the overall feel of the piece, there was still the requirement of contrast between movements. This later work still provides the contrast.
Why might you describe the later sonata as a Romantic work?
Opus 111 breaks away from the more rigid requirements of the classical sonata in being presented in only two movements. The romantic era imposed fewer restrictions on the composer, allowing them pure expression over a prescribed format, displayed in the second movement by Beethoven’s freedom from a single definite motif.
Read about and hear Op. 2 here.
Music From The Present To The Past 