Some of the Fire Emblem sprites were breathtakingly fluid, and you can't deny that they often look better than the jaggy polygons of the modern DS titles (similar to how the OP contrasts Final Fantasy Tactics Advance and Diablo).
My favorites were always the sprites for the "hero" unit:
Good point. Heroes probably had the best attack animations. Either them, or critical hit from the paladin.
My favorite animations overall though were definitely swordmaster, specifically their "dodge" animation. They only moved like 3 or 4 pixels, so it was hard to tell that they actually dodged. But once you saw it, it was in fact amazing.
My favorites were always the sprites for the "hero" unit:
http://vignette4.wikia.nocookie.net/fireemblem/images/3/38/F...