We've done it both ways...moving is not a big deal, but not moving is nicer.
When we were not moving, we told our stateroom host to not bother cleaning our room on "changeover" morning. We had been informed by GS that we didn't have to get off the ship (this varies from one B2B to another, and isn't the norm), so we were planning to sleep late and just ignore the commotion of disembarkation. He agreed, but then he cleaned it anyhow when we left to get our new KTTW cards.
When we moved, we were told to call GS when we were packed up and they would send someone for our luggage.
Each B2B seems to be different--I know that our instructions were different each time, and another board member reports doing 6 B2Bs with each different. The only thing I can tell you for sure is that you will get instructions in your room the morning before the change over, and that it will be as easy as Customs will allow them to make it.