Both composers are worthy of the title "genius", yet Beethoven's genius, as I am to claim in this abstract, is more universal and thus more profound of the two. In a few epithets, the bulk of Mozart's creation can be described as lightweight, springy and delightful, often evoking soothing and calming effects in the listeners. Undoubtedly, he reached unprecedented heights of proficiency in aiming at this particular sensory sphere and expanded its boundaries to a truly cosmic scale. But Mozart's music is purely entertaining, and, as such, it rarely crosses to the intellectual and more demanding realms of human perception; this is where Beethoven takes the scepter and rules unconditionally: opposite to abovementioned description, his music is often heavyweight, consciously brooding and hence dramatic to the point of tragic. Indeed, the broad comparison of the qualities of the comic and of the tragic comes to mind: the former deals with life and death issues with an aerial and playful approach, avoiding engaging philosophical delving, whereas the latter is more or less defined by an uncompromising probing of said issues. Mozart can be nostalgically melancholic, Beethoven can be woefully grim; Mozart can be charmingly gay, Beethoven can be strikingly passionate.
If Mozart communicates joy and even teaches us to experience it, Beethoven constantly seeks to reflect other, yet untouched (in music) aspects of the human condition, - and it is this search that he passes on to the audience. And this makes him the discoverer, the visionary and ultimately the deeper and more important composer of the two. Beethoven transcends music and stands out as a humanist. After sufficient listening, it seems that Beethoven is aware of the mozartian milieu, yet chooses to explore other territories - the opposite, however, cannot be said about Mozart. Listen to Mozart to relax, listen to Beethoven to wonder. *You are invited to read here on Rachmaninoff and Scriabin: http://www.shvoong.com/humanities/415751-com parative-composers-rachmaninoff-vs-scriabin/