The last time we switched, it was a while ago, they would not take it without us going along which was a real drag. In the past, they just moved it over for us to the bell station at the other hotel and we would just call for our luggage when we got into our room. We'd just tip the bellman who picked it up at the first hotel and the bellman who delivered it to our room at the second hotel.
But this last time, it went like this: call from room for bell hop, he comes and picks it up(TIP) and takes it to luggage hold where another bell hop(TIP) rolls it over to the other hotel's bell station. Then another bell hop checks it in there(TIP) and finally when you get your room, another bell hop brings it to your room(TIP again.) We had a LOT of luggage, maybe 5 bags and at $2/bag the tips were waaaay more than taking a taxi ourselves (under $10) and we had to walk along the whole way with the luggage taking more time out of our day.
Either bring rolling luggage you can walk over yourselves or take a taxi! There is NO formal charge but the tips are a killer....