I've played both games and the only immediate ones that come to mind is that depending on which version you're playing, stuff are gonna be named either sun or moon. Some examples is that flute thing, the altar place in the canyon and that lake place somewhere on the third island. Cosmog's final form also depends on which version you are playing. Solgaleo for us and Lunala for um and Necrozma will also absorb the version exclusive of Cosmog's final form. There's also a time difference that is absolutely a pain in the ass. If you're playing us, the game follows your 3ds clock but if you're playing um, it advances twelve hours. Say you're 3ds clock is at 8, the game will treat it as if it was 20
Of course, gamefreak's favorite way of milking as much coin from its consumers makes a return in the form of version exclusives and assume their entire evolution line for most of them is exclusive as well. According to this the exlusives for us are
Alolan Vulpix
Houndoom
Passimian
Turtonator
Buzzwall
Kartana
Cranidos
Tirtouga
Cottonee
Rufflet
Blacephalon
Ho oh
Raikou
Groudon
Latios
Dialga
Heatran
Reshiram
Tornadus
Xerneas
Totem Lurantis
While for um, the exclusives are
Alolan Sandshrew
Manectric
Oranguru
Drampa
PHeromosa
Celesteela
Shieldon
Archen
Petilil
Vullaby
Stakataka
Lugia
Entie
Kyogre
Latias
Palkia
Regigigas
Zekrom
Thundurus
Yveltal
Totem Salazzle
There's also a group called the 'ultra recon squad' and the guys you encounter will differ based on which game you're playing. Finally, the first totem Pokemon will also be different. Gumshoos for us and Alolan Raticate for um