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the "alternate story" is just the Ultra Beast storyline expanded to the length of the original story and merged with it
Necrozma is a Cosmog that evolved at the midway between day and night, similarly to Dusk Lycanroc. It first appeared in Alola in ancient times, in its Sunne Forme or Moone Form depending on the game, and is the first Ultra Beast. It was turned into its Prism Forme when the tapu stripped its power using the Guardian of Alola and buried it under Ten Carat Hill.
there are three new islands with Flying, Ice and Psychic specialist kahunas, every other type now has a trial associated with it
Royal Avenue and Grand Hano Resort have been fused together into one large zone. The hotel now has the minigames from Hotel Richissime in XY and can be explored
Battle Royal Dome has been expanded and repurposed to host PWT-style 8-man tournaments, but the only formats available are Single and Double Battle on top of the existing one-off Battle Royals. There are now five ranks, the original four plus a Secret Rank that uses only the special trainers from the Battle Tree. There are no Mix Battles, Rental Battles, or any of the other PWT formats.
Since the UB story has become the main plot, the post-game story now involves helping Looker, Anabel and Zinnia investigate rogue agents of the Aether Foundation seeking to capture Dialga, Palkia and Giratina.
Battle Tree is unchanged except for additional trainers: Zinnia, Giovanni, Lance, Steven, Cheren, Bianca, Diantha and Wicke
140 new Alola Dex Pokemon, divided evenly amongst the seven islands, primarily including the Mega Evolutions missing from the original game, minus Mewtwo and Diancie but including Rayquaza, Latias and Latios, who have small side quests at Mt. Lanakila and Aether Paradise respectively. However, there are more version exclusives in these games than in any other released before, including Latias and Latios.
Beast Balls now automatically catch any Ultra Beast