You can also save the cabinet from the rig you want to copy from . You load that rig, then drag the cabinet icon in the editor to Local Library under All Presets. You could also create folders under All Presets\Local Library for this. I've made a folder called Cabs that I can put cabinets in that I like. You can also add sub-folders to organize the cabinets.
You'd have to save cabinets one at a time to get them from rigs, but if you have IR's in folders you can just drag them into one of these folders.
Then as you load your other rig you can just double click the cabinets you've saved.
This is how I swap out and try different cabs as well! Saving the cabs you like from different profiles as presets, makes it easier to try out different ones.
This is probably one of the more simple and organized way of swapping cabs