It´s the same because the memory which stores than info is within the base, not the joy.
If you are swapping joys, with the same TM base, just save a DCS controller profile with the first installed joy, unplugg the usb, remove, install the other, plug usb again. Bind your things on DCS, and save a new profile. I have to, something like "Tundra_Warthog_v1", and "Tundra_Hornet_v1".
No need to reassign after every swapping.