If I understood your question correctly, you’re asking two separate questions:
What is more important?
A. Songwriting: Lyrics vs. Melody
B. Song sections: Verse vs. Chorus/Bridge/Intro/Outro and vice versa.
Lyrics vs Melody;
Tough to answer. A song without a decent lyric can get by, (Some songs go viral without lyrics in the first place, i.e. No Lyrics [Benny Friedman], a whole slew of 8th Day songs, etc.) but a song with a horrible melody won’t get off the ground.
On the other hand, a really good song has both. Abie Rotenberg’s work is a fantastic example of this, with both really beautiful, meaningful (and on occasion, witty) lyrics fused with fantastic melodies.
A song does not, however, really require an extraordinary melody to be a hit. Baruch Levine’s Vezakeini has, in my opinion, a really plain, ordinary tune,with nothing extraordinary going on (as anyone who plays an instrument by chord will tell you). Not a bad melody, just not an exceptional one. A really plain melody! Lots of repeating notes! And yet, the lyric, which is quite poignant in this day and age, is what propelled it to the #1 ballad (slow song) in Jewish music of the past couple years, along with the likes of Yossi Green’s Anavim and Shwekey/Yonatan Razel’s Vehi Sheomdah, both unique songs (both in melody and in lyric).
So what is more important? Lyric vs melody? Given a choice of one or the other, I’d reluctantly say melody. Realistically, you really need both for a good song, along with a good arrangement (intro/verse/chorus structure; precise chord pattern), orchestration (choice of instruments), vocals (which singer, vocal effects, choir or not, if so, which size adult vs children), and other miscellaneous bits and bobs such as “feel” (laid-back vs upbeat, regardless of tempo [song speed]) and choice of musicians.
And verse/chorus structure?
Hands down, the chorus is the most important part of the song. The chorus is the song. Imagine Ma Ma Ma, Anavim or Hofachto without the chorus! Without a chorus you’ve got nothing.
Some songs have a hybrid style, such as Kach Es Sheli with a blended chorus/bridge.
The chorus is the heart (like the bass in orchestration). Everything else is mere detail.