What is the difference between the two "worlds" when going thru the day/night wormhole at the altar?

Solution 1:

In order to open the portal, you need to have the legendary Pokémon that commands the time you're trying to get to. If you want to change the time to daytime, you need Solgaleo in your party, and if you want to change the time to nighttime, you need Lunala in your party. This means that without trading, you can only travel through the portal during real life nighttime, but if you have both legendary Pokémon, you can change the time at will. You can also always return to the world you originally came from.

The only differences between the worlds are the time, and an event which

lets you obtain Cosmog at the Lake of the Sunne in Sun and Lake of the Moone in Moon.