I've never stayed at POP, but my one experience at All Star Music was a thin-wall nightmare. I've stayed at Mods and Deluxes at WDW, but this was the only Value I ever experienced. I could hear everything the people in the next room were saying and doing. They were speaking in normal voices, not shouting. The noise may have had something to do with the fact that there was a connecting door between the two rooms, but even though I've had similar setups at other WDW hotels, I've never had that experience. And because of that, I've never stayed at a Value resort since.
So I don't think the room-to-room noise level is the same everywhere.