Even though Beethoven is included with Haydn and Mozart as a Classical composer, how does his style differ from theirs?
In my mind, the later periods of Beethoven's work is where we see a greater separation from the Neoclassical composers of Haydn and Mozart. Beethoven appropriated a much larger social message to his work with the fluid political scene of the time period, as well as the infusion of drama to his work. Beethoven was able to compose large level symphonies about heroism and pitting the individual in the midst of challenging social situations. Beethoven saw a dramatic element to his music, something that the Neoclassical composers did not envision. The Ninth Symphony's backdrop of Schiller's work "Ode to Joy" seeks to make a statement about what it means to be human through music. This conception of artist and their place in the world and how their art can comment on both is something that was not envisioned during the Neoclassical period.
When he moved to Vienna to study with Haydn in 1792, Beethoven earned a reputation as an outstanding pianist and, as a pianist, became the darling of the Austro-Hungarian aristocracy. These early years in Vienna were also significant for his compositional career. From 1792–1803, he produced, among many other works, the Opus 1 Trios for Piano, Violin, and ’Cello; the Opus 18 string quartets, and the Symphony No. 1 in C Major. In 1801, Beethoven’s career and finances were flourishing, but he was in poor health. His hearing loss was becoming progressively worse, and Beethoven grew increasingly depressed and panicked about it. His emotional crisis came to a head in 1802, but served as the creative catharsis for his second rebirth in 1803, in a self-sufficient and heroic guise. Due to his weakening condition, Beethoven redefined himnself and redefined the classical period.
In 1802, Beethoven was poised to reinvent himself as a hero, struggling against his fate. His "model" for this new self-image was Napoleon Bonaparte, who at the time, represented a vision of individualism and empowerment. Beethoven’s music reflects this vision in its insistence on expressing the heights and depths of the artist’s emotions. His Symphony No. 3 in Eb Major, Op. 55, for example, was nothing less than revolutionary in its grand proportions and dramatic expressive content. This first of the so-called "Heroic Symphonies" changed the history of Western music. During this so-called "Heroic" compositional period, from 1803–1812, Beethoven produced such masterworks as the Fourth, Fifth, Sixth, Seventh, and Eighth Symphonies; the five middle string quartets; the Mass in C Major; and the opera Fidelio.
Toward the end of this period, however, Beethoven experienced a short-lived affair with the "Immortal Beloved," which ultimately precipitated his fall into four years of despair, destruction of his brother’s remaining family, and public ridicule.
In 1819, Beethoven used these events, once again, as a catalyst for an artistic rebirth. In the last years of his life, he wrote many of his greatest, most profound, and most "modern" works, including the six late string quartets, the Ninth Symphony, and Missa Solemnis. Beethoven’s Symphony No. 9 became the single most influential piece of music composed in the nineteenth century.
The work breaks with time-honored conventions and distinctions to give precedence to the expressive needs and desires of the artist. During these last years, Beethoven was consumed by his craft but still difficult with friends, family, and business associates. He died on March 26, 1827, having reconciled himself somewhat with his family, and was given a loving tribute by the people of Vienna.