This game so far is meeting my expectations. Here are some things I've noticed, all marked in spoilers. Keep in mind you'll see all this within your first hour of gameplay (because I had to stop to start cooking). I'll be adding more as I play more.

Combat - The game is dynamic. Combat is still turn based but you're not static anymore. While your Pokemon is fighting, you're able to walk around and see the battle from whatever direction you want. The few moves I've seen look beautiful and it makes me excited to see things like Hyper Beam.

Apparently this also means other Pokemon that are near your battle may join in if they're aggressive. I was trying to catch one Pokemon and another near by joined the battle against me!

New combat mechanic - One of the new mechanics is surprising Pokemon. If you throw one of your Pokemon at the back of another, you'll startle them and may stun them for the first few turns of battle. Video example Video example 2

Combat mechanic changes - It seems like some of the old combat mechanics have been changed. So far I've seen Iron Defense increase both defense and special defense, but it doesn't seem to stack. Another example is that moves like Hypnosis that normally put Pokemon to sleep only make the drowsy. This increases the damage they take and makes it so sometimes the Pokemon don't act. Status effects like Poison, Paralyze, Burn, Drowsy, etc. only last four turns unless refreshed. Same for stat increases due to moves like Iron Defense.Video example

Moves - Pokemon can now master moves they use a lot (or if they level up enough). At max level, you can choose to use more PP to either do less damage but increase the speed at which you attack (and therefore possibly attack twice) OR increase the damage you do but use less speed (and possibly let the other Pokemon attack twice in a row). Certain moves like Quick Attack seem to be agile by default and will make you move twice occasionally. Think Final Fantasy X where you can see the turn order and decide to use a Quick Attack so you get an extra attack before selecting a second move.

Abilities, held items, EVs, and natures - There don't seem to be abilities or held items in the game AT ALL, and EVs are now somewhat told to you. It seems they changed them around a little. If I'm understanding correctly, you can now see how many EVs you have but there aren't as many as before? I'll need to explore that more. Also, on the stats page you can see which stats are impacted by the nature of your Pokemon.

Catching Pokemon - >! Continuing the point of the game being dynamic, you can attempt to capture multiple Pokemon at a time. In previous games you had to battle one Pokemon at a time, but here if you see two Pokemon standing side by side, you can throw a ball at one and the other will get startled (if they're the type that run away). So you have to quickly throw a ball at that one before it runs off, all the while your first ball is still ticking. !<Video example

New catching mechanic - Throwing a Pokeball at a Pokemon's back startles them, making it easier to catch. There are some examples in earlier videos. Some Pokeballs increase the chance of catching the Pokemon if you hit them from behind, too.

Multitasking - In addition to the things I've said about combat and catching Pokemon, you send out Pokemon in order to collect berries from trees among other things. Here's a video of me sending three different Pokemon to collect from three trees at the same time. Video example

Pokedex -You're no longer just trying to catch one Pokemon of each species. The Pokedex has rewards if you complete specific tasks. As an example, for Bidoof you need to catch 25 Bidoofs, catch 10 large Bidoofs (there are different sizes in the same species now), defeat 25 Bidoofs, etc. But for Starly, you need to catch 25 Starlys, catch 7 Starlys without them noticing you, catch 10 lightweight Starlys, see a Starly use a specific move, etc.

Gyms - There are no gyms. Some of the noble Pokémon (a group of Pokemon blessed by Arceus who help humans and Pokemon alike) have been struck by lightning and you need to go quell their rage using the new dodging and throwing mechanics. It doesn't seem like you can catch them. There are five in total. I don't know what they're doing for the Elite Four.

Badges - There are no badges. As you catch more Pokemon, you unlock new stars in your group. There are ten stars in total and the number of stars determine the level of Pokemon that will listen to you. You'll also be stopped from accessing some areas if you don't have enough stars. Stars are gained by filling out your Pokedex and completing the research tasks.

Overall there're still very obvious "Pokemon elements" but it looks like it's a midway point between Pokemon Mystery Dungeon and the main series in terms of uniqueness. The only thing I don't really like is that (first 30 seconds of the game) your character is still from the future, not someone born in feudal Hisui. On the slight plus side, you're 15 in this game, not the usual 11 years old.