KanataEXE hmmmm..... depends on the situation. I do find myself using both.
I prefer sprites for animated movement because as long as your code is right, it will play right. I even use some animated sprites in UI just because of how easy they are to drop in.
When I need to do movement that do NOT involve the sprite changing, I use AnimationPlayer (positions for cutscene objects, shaking environment pieces, etc.).
I feel, for structured, sequenced animations, the AnimationPlayer is better. But if you have a graphic to change fully, use AnimatedSprite. It's also very easy to change the elements of a Sprite vs an Animation.