Just to answer this question- no, they generally don't become stressed when moved from a tank to a tub. A tub is in itself a more secure place than an open glass tank.
Some keepers have experienced their bp's becoming more defensive when moved to a tub from a tank, but only when the tub is removed from the rack. If this happens, my theory is that it's so much more secure and dark in a tub, and not being exposed to outside activity, that when the tub is removed from the rack and hits the light/suddenly there's a looming figure, it's more of a shock... so may cause defensive behavior, if that makes sense. But after awhile of getting used to it, the defensiveness goes away.