If I put my Pokemon Moon game into a different 3DS than the one I started filling the VIP and guest list on, will my game's VIP and guest list be the same on the new 3DS, or will they be lost? (Like how in Pokemon X and Y changing the 3DS would forget all friends.)
Yes, you should keep them.
All 3DS physical games are saved to the cartridges they are played on. Only digital version games are saved to the system memory.
Some games do save SpotPass and StreetPass information to the system memory, so you may lose only those random users in your Festival Plaza.
Source, Nintendo support.