What's really interesting is that while A SONG IS BORN works from (obviously) a slightly modified script and has a different cast, it shares the same director (Howard Hawks), the same director of photography (Gregg Toland), and the same set decorator (Julia Heron). This means that a lot of the scenes don't just play out in very similar ways; they *look* very much the same; they were shot six years apart, but the professors' home looks so much like the same set that it's mind-blowing. Where there are differences, they're usually improvements -- you can tell that the filmmakers thought about what they'd done, kept what worked, and changed or fixed the stuff that bugged them, or they thought they could do better, or just needed minor adaptation. The only film experience I've had that came close is watching the Spanish-language version of DRACULA, which was filmed at the same time as the Browning-directed Bela Lugosi flick and used the same sets, shooting at night, when Browning's cast and crew were off work. That was weird -- same costumes, same sets, but in some cases radically different directing and acting choices. There was more unity on A SONG IS BORN/BALL OF FIRE, understandably, but it's an interesting thing to see.
Side note: a couple of cast members were in both flicks. Mary Field, often typecast in spinster or nosy roles, played the spinster Miss Totten in both films. And Will Lee played "Benny the Creep" in BALL OF FIRE, and appeared uncredited as a nightclub waiter in A SONG IS BORN. He, of course, went on to greater things (video).