Huge changes to the pokemon formula since Pokemon X & Y, no longer as it's strictly battle and collecting focused (although still present) as they added variety of mechanics to switch things up a bit and to bring more variety in gameplay. Changes include:
1. No HMs
No longer do you have to carry around a HM slave (s). This has bothered me in the past games as I have to restrict 1 or 2 slots out of my party of 6 to help traverse certain areas of the world. In the place of HMs there are Poké Rides where you can ride pokemon interacting with them on the world map, some you may not be able to access until you've completed mission within the game.
2. Is it super effective?
No longer do you have to look up guides online (unless it's your first encounter) to tell if a move is super effective or not very effective against the pokemon you're up against. After you battle a pokemon once, the game will tell you what moves is super effective or not in the battle menu once you encounter the same pokemon the second time.
3. No Traditional Gyms
No longer do you have to battle your way through gym after gym to prove you're the best out of brute force.
There are 4 islands in the game, each of which are controlled by 4 Island Kahunas
To get to them you have to get pass Trail Captains and Todum Pokemon
Trail captain will give you quizzes, side quests to complete, and/or fight in traditional battles
Todum Pokemon. Basically typical pokemon you find the wild, but significantly stronger and have grunts that help them battle.
4. Rotom Pokédex
Typical pokedex, but with a face and personality attached to it.
5. Alola Forms
Basically different forms of pokemon you seen in previous generations. Either it's there physical form that is different and/or the pokemon's typing
With a Z-Ring and a Z-Crystal you can use a pokemon's ultimate move once per battle. It's not like Mega Evolutions where it stays constant
7. QR Scanner.
You can now scan QR codes to get event pokemon. Also if you scan a random QR codes it will give you 10 points. Once you reach 100, you are able search an island for a rare pokemon. Each scan also gives you random trivia about pokemon
8. Battle Royal
A 4 player free-for-all where the battle ends after all of one's pokemon trainer's faints. They tally the win-losses of each trainer and the one with best stats at the end wins
9. Hyper Training.
Once a pokemon reaches level 100, they can go through hyper training which can improve a Pokemon's IV
10. Poké Pelago
Your PC Box now has functionality to it. It's like a day care sort of thing, instead of just depositing your pokemon, you can passively train them in the PC or have them search for items
11. Festival Plaza.
An online mode where you can battle other trainers and trade with them. You get festival coins for each interaction which you can spend on clothes, shop or upgrade your pokemon's stats. There's also missions you can undertake to get more coins.
12. Night and Day phase, New Pokemon
Pokemon Sun goes the traditional time route while Moon does the opposite. In Pokemon Moon if you're playing in the daytime, the game will consider it night time in-game. Some events also play out differently like different Totum Pokemon on the same island/trail
In traditional Pokemon fashion you can only get some pokemon in each version so trading is required either with a friend or if you own both versions. Also some pokemon evolve differently in each version now.
I'd say some of overall models of new pokemon are better looking than the last batch in previous iterations of the pokemon series.
13. Auto Run
Your run is as fast as a bike now, and it has unlimited use. You can now move in all directions instead of the traditional 4 and it feels very fluid
14. No Rod
Fishing is now dedicated to specific regions in the world. You cannot fish wherever you want anymore.
15. Photo Taking
You can now take Photos of pokemon in the wild.
16. Team Skull and Aether Foundation
Team Skull is the new antagonist group like Team Rocket, but they have a new style to them as they try act gangster-ish with their animated hand gesters/movements. They have more personality and have a darker tone to their backstory and mission.
Aether Foundation is the opposite of Team Skull as thier mission is to cure injured and hurt pokemon. The group is also conducting research on the Ultra Beast (Pokemon) which is a good mystery story in and of itself.
17. Graphical Upgrade
Game looks better than the last, although there are some pixelation around the edges still. Models look more realistic than before, and the battle animations are more visually impressive. There are some framerate issues on 2v2 battles for some reason, but then again I own the launch 3DS. You may not have the issue if you own the New 3DS? It's a turn-based system so it doesn't really matter much in terms of gameplay, but the slow down is noticeable
Pokebank return, you can now transfer all your pokemon to Sun and Moon
Clothing Options: Although more options are available, it still feel very limited.
Mega Evolutions return, but none for new pokemon from what i've discovered
Pokemon Refresh: don't remember if it's in the last game, but you can groom your pokemon in your party
If you discover more changes, please put in comment below.
Overall, love the changes to the traditional formula as it gives the Pokemon Series a nice refresh and is more streamline to play.