I think Im tired of the whole "evil team" as the main antagonist and build to the box legendary. I have a couple wishes that I doubt will happen, but I can dream
1) 2 or more evil teams in a "gang war" type of scenario, kind of like emerald, but not "theme" based. I think a "turf war" story can be cool and is easier to relate to in modern times. maybe both are going for one legendary (whichever respective legendary for each version) to wipe other the other(s) if you need the team to involve the legendary.
2) No evil team, just one antagonist who is really evil. Maybe add some humor that he tries to make a team, but he's too nuts to follow. That makes more sense than a huge mass of people that want to follow some guys dream to flood the entire planet earth. (Note: I feel bad for picking on Gen III but its such an easy target here)
3) Maybe the legendary is very wild/sentient and evil (or wild in one version and sentient in the other) and on the verge of destroying the planet, and the story is you building your way to save everybody and everyone doubts you. Maybe in sun and moon, one could be feeding energy from the sun and going haywire (sun) and the other can be more graceful, sentient, and focused on cleansing the earth (moon). To earn the right to fight them, you have to prove yourself through the pokemon league or something. I think this is my favorite idea because it would make the games seem so different, like night and day (ba dum tsss)
3.5) If there HAS to be a team in idea #3, make it like a team that is forming to save the world and sees you as a meddling kid and tries to stop you from your ambition to save the world. Then you'd seem more rebellious and give a mute character some life or something. Idk, just a thought.
But what I think will happen?
probably what they've been doing: one team shared in both versions that have some sort of anti-human/nature agenda and lead up to the version's box legendary. I'm a pessimist. If I'm wrong and they do something new, I think #3 (not 3.5. :/) of my desires is most likely to happen because the anime does it sorta like that (like with the deoxys movie)