Swapped myself the other day after maxing out. The first time you switch it will be free (there was implied to be a fee on further switches), and you will essentially start over in your new GC. I can still see all my seals from my previous GC on my character page, so it looks like all your progress is saved for each individual GC.
Sounds like how Conquest worked in FFXI, where you could change national allegiance, and have to start from scratch ranking up with them. And if you ever decided to switch to a previous nation, all your efforts remain intact there. (Started in Sandy, rank 10'd in Bastok and Windy, and moved back home to hang all 3 flags in my Mog house!)