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The switch to 3D was a necessity, but here's the way I see it:
The sprites were fantastic most of the time because of the dynamic poses many of the pokémon were drawn in. You use your imagination all the way until the animated sprites in Gen 5, where even then the aren't limited by the boundaries of 3D space. So they can make these wacky dynamic poses and animations. However, as screen resolutions became higher, sprites quickly became obsolete. Pixel art is, after all, just low res illustration. At some point you need to wonder how big to make the sprites for the high resolution screen, and it becomes obvious sprite work isn't going to cut it anymore, unless you want outdated graphics and/or poor animation flexibility.
The switch to 3D was obviously necessary, but the most glaring difference in quality is the lack of dynamic poses among the pokémon. This is due in part largely by the restrictions of a 3D world. Take Meowth's sprites for example. You can't just have a Pokémon standing on one foot as if it were jumping at you anymore. It's just not gonna look right. What needed to be done was dynamic animation to pick up the slack the dynamic poses left behind. You can have that "jumping sprite" pose if you actually have that Pokémon's idle animation perform some jumping. Instead we have Meowth with two feet planted firmly on the ground arms to each side, looking in one direction. That's the bulk of the problem. There are SO MANY pokémon just standing around in battle. The low saturation doesn't do anything good for the boring animation.