Pokémon Sun and Moon's improvements to the main formula as well as fixing past nuisances makes the streamlined experience much appreciated for both veterans and newcomers alike. This can't be stressed enough how refreshing it feels to what some consider to be the most visually appealing region in the series.
The transition in to a full 3D non-grid based movement has finally made it's way to the main series. It feels fresh moving around and the landscape itself has changed for it. There are no pointy corners and even the trainer encounter field of view has gotten an overhaul. Alola as a region is the most varied we ever had and still has it's own identity, it's not just another Pokémon Region, it has a story to tell and the visuals really help this.
The most notable change to the formula is from Gym battles to the Island challenge.Instead of going town to town fighting gym leaders with a puzzle or two, Island Trials give you a much different objective with their Trial leaders. And it's the fact that it's never expected, every island has their own amount of Trial Leaders with trials you must go through to pass. These trials are filled with a ton of variety of what it is your going to be doing. Some may ask to find ingredients or to chase a certain Pokémon or to watch a dance and find the difference. The variety makes sure you never feel dull, but it's not fully random, the Island challenge still follows a set of rules. After finishing a trial, your made to fight against a large powered up Pokémon called a "Totem Pokémon" who can call for help, similar to how other RPG's do boss battles which can get pretty challenging if your not prepared. After completing all the trials and fought the Totem Pokémon in an Island your faced against the Kahuna's which are basically the strongest trainer in the Island.
Z moves are another new addition, give your Pokémon a Crystal to hold (which are obtained by completing the trails) and they are able to use a powerful attack but it varies with what attack your choosing to power up. They work pretty well and are more balanced but they become annoying if your the type to constantly use them due to the long animation your forced to sit through even if you turn off battle animations.
I mentioned earlier about summoning a helper Pokémon, this feature isn't just exclusive to Totem Pokémon but rather wild Pokémon are able to use this and can overwhelm you if your not prepared. These encounters give other Pokémon chances of appearing that otherwise wouldn't normally but if your busy trying to capture a Pokémon, it'll give you trouble since you need to defeat one to be able to capture. The two mentioned are the only real issues but they are easily nitpicks and don't effect the enjoyment of the game for the most part.
Among the new Alola Pokémon are redesigns of Gen 1 Pokémon known as Alola forms. These in my opinions are a much better solution to making something new with something familiar, Atleast compared to Mega evolutions. It's interesting seeing these environmentally changes Gen 1 pokemon alter their designs and typing and are considered seperate Pokémon from their regular forms. Story in Pokémon isn't really huge, the highest point would have to be Gen 5. That being said Sun and Moon has an interesting way of telling a story.
Mentioned back in the beginning, Alola as a region is really interesting and you slowly learn more lore as you go on about this region, as well as the characters are easily the most fleshed out and personality filled in any game. Whereas Pokémon Black and White had a more story heavy focus, the only character benefitting was N, whereas in Sun and Moon, the major cast are filled with personality and interactions and they keep you interested in learning more about the Island and what they are doing. Again, nothing too overwhelming by Pokémon standards, the story still falls in expectations, but the characters making you a story was much more inviting then simply following a set up story.
Among the stated above, Sun and Moon also pushes a ton of little changes that greatly improve the experience that bothered past games. First it'll, HM's are entirely gone and replaced with Pokeride which is easily accessible and don't force you to carry a nuisance Pokémon for the job. Pokémon Palego makes great use of your otherwise barely used PC Pokémon by giving them a job that can give you items, berries, beans to trade and even to just train in general to level up. The daycare center has also been changed to be specifically for breeding since Palego levels your Pokémon up. There's also the Plaza that gives a ton of online interaction options and tent mini games.These normally don't get much attention but as a whole the streamlined approach is extremely welcome and makes the experience wonderful.
In conclusion, it's Pokemon's 20th Anniversary and this game is the culmination of how The series has progressed with a game that not only pushes this forward but also incredibly accessible for all ages. Here's to more incredible years for Pokémon.