Which bottle empties first? The motionless bottle or the bottle being moved in a circle? I tested this out with my girls the other day and here is our video.
Yes, that is a bottle of flavored Smirnoff Ice. LOL!
It's a bit tough to see from the video, but the circling bottle empties slightly before the stationary bottle. Why? By moving the bottle in a circle, the liquid inside isn't pouring straight out the bottom of the bottle. It twirls around the edges, leaving a gap in the middle for air to more easily enter. In this way, it's similar to tipping the bottle slightly when pouring.
Try it out yourself. You may find using two liter bottles to be more effective. I'm not sure, but it's something we may test out in the future. With more liquid initially in the bottle, there may be a greater time difference at the end.