I only listened to "Door Number Three" once before today (right after the first time I watched the show, so really biased and in love with "What Baking Can Do"
so I really wasn't a fan of "Door Number Three."
I just listened to both songs again, and while I still like "What Baking Can Do," I think it's a much closer call. Musically, "Door Number Three" is a much more obviously a Sara Bareilles song and, much as I love the "What Baking Can Do" bridge, I think I actually like the "Door Number Three" better. However, I think what bothers me most about "Door Number Three" is the door metaphor. I get the "she chose one door and regrets it, but can't" idea, but the "choose the door" concept just - to me - feels really carnival-y and jarring compared with how the song sounds and every other lyric in the song.
By now I've listened to "Door Number Three" at least five times in a row, and it's really a beautiful song, but I still don't think the door number two/three theme works very well.