Phew! What a subject...
The way I see it:
Mozart single-handedly turned events over, in all genres.
With him, what we call the repertoire was created.
He became the first composer in history to be continously played. First in his own lifetime, then in the following century (the 19th), then in the next (the 20th) and is still played (the 21st). And this is in every genre. Opera, church music, symphony, concerto, chamber music, duo-sonatas, piano music, songs.
One couldn't argue that he is superior as a composer to Bach, except possibly in one respect: the absolute mastery of each and every genre and instrument possible and available. Mozart stands alone in history there.
Nevertheless, historical events played their role in his posthumous fame. As often said, the french revolution created, politically or idealogically, a middle class throughout Europe, who strongly yearned to up themselves culturally and intellectually. In other words: more people had more money, time and interest in participating in what was previously more exclusive to the ruling upper classes in society. In music, taking interest in the most highly regarded composers and instrumentalists fit this desire. And none more so than the newly deceased Mozart.
Beethoven follows. He had the benefit of being able to build on, learn from and get inspired by Mozart. And of course Haydn, and his pianistic favourite, Clementi.
In short, he had one great genius to look up to. Mozart didn't have that.
Mozart discovered Bach late in his life. Beethoven always knew about Bach's WTC, but only later in life started to incorporate polyphonic lessons learnt from that into his own composing.
Nevertheless, Beethoven stands as the very center of gravity in music history.
He can not be said to be as diverse in genres as Mozart. But where he is most supreme, in symphony, concerto, string quartet and piano sonata, he not only created "perfect" works of art: he virtually goes as far as to virtually finish these forms off.
I firmly believe that no musician after Beethoven can escape his influence, consiously or unconsiously. Whether you be a Jimi Hendrix, Yngwie Malmsteen, Franz Liszt, Johannes Brahms, Wagner, Schostakovich, Prokofiev or Sviatosvlav Richter, you're still identifying, or the audience is identifying, with the idea of the "demonic virtuoso" or the "demonic master". And the original "demon" is Beethoven. Not only in composition, but also in "image".
Bach fits into all of this of course, but the particular historical "problem" here is that he lived in an era where musical performances were supposed to always consist of new compositions. Fame consisted more of reputed merits and current compositional and improvisational skill, rather than repertoirinal knowledge. Hence, Bach was "rediscovered" during the romantic era's preoccupation with repertoire. In Bach's case, the 1840's.
This is only shortly discussing three famous names.
I like a sentence I read in some book. It went something like: "musical mastery can never be improved upon with subsequent generations. It can only find new expressions."
So, Wagner operas might be louder in decibels and require a larger orchestra and bigger-voiced singers than Mozart's operas, but are they greater compositions?