Definitely silence, here. Glad to know I'm not alone as I've been feeling a little inadequate for not being able to stay productive when I have free, but chaotic time.
I have a hypothesis as to why this is the case for me- When I think, I "hear" a voice in my head much of the time- esp. when I'm thinking about words. I hear the same thing when I read a book. If I read a letter from my mom, I hear it in her voice. It's all very much like movie voiceovers. I think noise disrupts this voice in my head, and thus, my ability to process information. My husband, on the other hand, never hears a voice. He just thinks as an action and reads in a way he derives meaning without needing this translator. He can work in chaos with music blasting, car alarms outside and me banging pans and pots.
I've done informal surveys in the classes I teach and about half my students hear the voice; half don't. One way of coping that I've found is to listen to instrumental music (like soft jazz or classical)- it seems to stay in the background. Music with lyrics disrupts me (I guess, again, because it sings over the voice in my head).