While this list is likely not 100% complete, these are all of the differences I know of. I will add more if more are found.
POSSIBLE SPOILERS BELOW
Version-Exclusive Pokémon / Ultra Beasts
Sun: Passimian, Tortunator, Lycanroc-Midday, Alolan Vulpix, Alolan Ninetales, Solgaleo, UB-02 Expansion
Moon: Oranguru, Drampa, Lycanroc-Midnight, Alolan Sandshrew, Alolan Sandslash, Lunala, UB-02 Beauty
UPDATE: Today's CoroCoro leak showcased two more Ultra Beasts, Kartana and Celesteela. Above Kartana was a picture of Sun, and above Celesteela was a picture of Moon. While there is no confirmation that these two UBs are version-exclusives, it appears to be that way.
• The clock for Sun is set normally relative to our world. Noon in real life is noon in the game, etc.
• Gumshoos is a totem Pokémon.
• Events of the story revolve around Solgaleo.
• The clock for Moon is 12 hours behind ours. Noon in real life is midnight in the game, etc.
• Instead of Gumshoos, the totem is Alolan Raticate.
• Events of the story revolve around Lunala.
As far as I can tell, that is all.