Green Album, Wagner, Mozart
Although I am no authority, it is my understanding that "Zauberflote", "Figaro", "Don Giovanni" and the handful of other Mozart operas are considered to be among the greatest achievements of Western music . Wagner's work, on the other hand, is generally credited with being the most obviously erosive factor in bringing music down from its high point in the eighteenth century.
Listen to Zauberflote. What you hear is an amazing collection of pop songs, all perfectly crafted and arranged in a dynamic and organic way, sustaining a pleasurable listening experience for over two hours. The songs don't try to carry the plot of the opera. They're just beautiful songs. The plot is carried along by the recitative in between the songs.
Wagner, on the other hand, eliminated the song-form/recitative combination and strove for a continuosly developing composition which could last, literally, for twelve hours. There's no catchy tunes, there's no satisfying choruses, there's no rousing rhythms. Why? Because, for Wagner, music now only existed to describe the events of the plot. The composition was no longer essentially musical, but rather dramatic. Therefore, Wagner's "music" is decadent in the sense that it no longer adds up to a solid musical composition, but rather of a series of dramatic, and occasionally thrilling, effects.
This leads me to your question about Stravinsky's Firebird, which, as you pointed out, tells a story. Stravinsky rejected the decadence of Wagner's music quite vehemently, and self-consciously modeled his music after the Classic masters, like Mozart. For example, he utilized the song/ recitative structure of the eighteenth century, even going so far as to utilize the dorky harpsichord flourishes in between songs in his opera "The Rake's Progress"! The result is a neo-classical opera; a complete rejection of all things Wagnerian. Green album, anyone?