I have ridden in the A320 a lot, when I was working in Munich and going back and forth with LH for 18 months.
I have sat all over the place and never heard no popping!!! Of course, I might simply have ascribed the noise to the gear doors closing and so have thought nothing to it.
The flaps are no noiser than on 737s, I would say. The noise that most people comment on (and there was a thread recently) is the particular engine noise at t/o. I cannot recall which manufacturers engines it is, but there is a highly distinctive whine when they spool up. Also, on final. As I say, I know what they are, so it doesn't bother me and I will tell any anxious pax next to me.
Now, what about the noise of BAe 146/RJ flaps in transit? Not to mention
their gear doors.