your Freind Safari is based on your 3ds FC,hence changing your 3ds will change your Friend Safari. However the safari of other people(ie the pokemon you see in the safari) will remain same assuming you have the same friend list in the other ds.
If the two systems have different Friends Lists? Will each one maintain a separate FSZ when I switch the game to that system? Also, would I keep any "third Pokémon" found when I switched back to the original system? Or would I have to be logged in at the same time as my Friends again to re-unlock them?