I've checked the obvious: opening dates, closing dates, # of performances, etc. He said it has nothing to do with casts or plot lines. I will post the answer tomorrow.
There's a happy little flute riff that's part of both these songs. It's discussed in Ted Chapin's book Everything Was Possible: The Birth of the Musical Follies.
"During Waiting for the Girls I heard things in the flute and piccolo that reminded me of Bye Bye Birdie. They came during the women's chorus, adding a playful punctuation to the ends of their four descriptive lines. They reminded me of the flute passages from "Put on a Happy Face". I asked Jonathan Tunick about them and he said 'Ah yes. The Ginzler flutes'. Ginzler was the orchestrator of Bye Bye Bridie and one of Tunick's mentors... in the hands of a good ochestrator there's room for appropriate musical quotes or references. Little ornamentations or jokes that can be added and invisible except to those knowledgeable about musical theater."
Me too, lovebwy. Many arrangers like to bring out the Ginzler flutes when appropriate: Jonathan Tunick did it again for "Manhattan" in Stairway to Paradise. And I hear an instance on Philip Chaffin's newest CD from PS Classics. There's also a startling pre-example in the title song of Louisiana Purchase (1940).