My headcanon is the Ocarina of Time is bigger than Fairy Ocarina. Link needs to use it to open the door in Temple of Light, then uses it as adult because it's a better fit for his hand. When he goes back to being a kid, he uses Fairy Ocarina for anything not Hylian Royal Family related. Or keeps it at his house since it is precious to him and he doesn't want it to get destroyed during battles.