The assumption of the Art Song (in the musicological literature) is that the text comes first, and then the setting later, so that we can study the text itself (By Schilller or Goethe) and then see what the composer did with it. I guess this is accurate, and yet...
1. The experience of the listener is simultaneous. The reader does not first read the poem, interpret it, and then hear the musical setting. She might encounter the melody before the words, if she's heard instrumental versions before hearing the song sung (as happened to me with "Blue Skies" by Irving Berlin.).
2. In the popular song tradition [in many vernacular traditions], we don't give priority to the text over the setting. We simply don't care whether the lyricist wrote a lyric to a melody, or whether the lyricist and composer worked simultaneously, or whether the composer and lyricist are one person, or whether the composer set a pre-existing lyric to music. In folklore we have songs that come with their words and melodies together, and nobody cares what came first.
3. Words are not prior to music ontologically, then. Putting words first is the artifact of a particular musical tradition. Nevertheless, this tradition is extremely significant, because, well, we have very significant poets being set to music by equally significant composers. Aside from the Lied, there is the French mélodie.
4. Do we put more value on the music than the words? It depends. If we have Baudelaire and Debussy... Do we have to think that George is greater than Ira? (Because Ira's rep as a poet is less than George's as a composer?). I admire song lyrics because I cannot write them very well.