With regards to animated acting, I've written that I don't believe the technique (meaning drawn, cgi or stop motion) is responsible for the quality of a performance. What I believe is that a character has to be conceived with an inner life and a certain measure of complexity before a good performance is possible.
I'm going to start with some live action examples, though they're not particularly current. In the 1930's, Humphrey Bogart was almost always cast as a gangster. These characters were one dimensional, usually nasty and violent. Occasionally, the character would reveal cowardice when he was about to die. To use Dorothy Parker's comment about Katharine Hepburn in another context, in these roles Bogart ran the gamut of emotions from A to B.
In 1940, Bogart was cast as a gangster in High Sierra. There are major differences in the way this character is conceived. Bogart is shown to be weary. He is disappointed several times in the film by the world treating him worse than he deserves. He sees his options disappear as the law closes in. The character's end is tragic; he's finally found the loyalty and emotional support he craves, but it's too late. Bogart's death in this film resonates emotionally in ways that his earlier deaths never did.
Bogart the actor did not suddenly get better; he merely got a better role. It was better because the character had a history, a point of view, and self awareness; in short, an inner life. Bogart's character in High Sierra is a complete person, not merely a few traits assigned to a role in order to advance the plot. After High Sierra, Bogart continued to get better written roles.
This process can also work in reverse. During the 1920's, Buster Keaton worked for producer Joseph Schenk. Schenk was a hands-off producer who left Keaton alone to create films the way he wanted to. The plots of all of Keaton's features in this period follow the same pattern: put-upon little guy makes good; gets girl. Keaton varied the settings and often built the films around large machine props like locomotives, ocean liners and steam boats, but stuck to the formula.
In 1928, Schenk sold Keaton's contract to MGM. The producer there, Irving Thalberg, was the opposite of Schenk in that he involved himself in every aspect of the studio's production. MGM and Thalberg considered Keaton a performer, not a film maker. At MGM, Keaton's scripts were created on an assembly line without his input. They didn't understand that Keaton's success depended as much on the construction of Keaton's world as it did on his performances.
In truth, while Keaton was a marvelous acrobat and had a fine mind for gags, he was somewhat limited as a performer. Keaton the performer depended on interacting with a universe that was a giant machine, indifferent to its inhabitants. Keaton's appeal came from his ability to overcome physical obstacles on the way to achieving his goals. Social situations were not the root of Keaton's comedy, and Keaton's sound films were all built around social misunderstandings and threats.
Like Bogart, Keaton did not change as a performer. In Keaton's case, the character's relationship to the universe was taken away, leaving his character with nowhere to go.
On the animation side, Bill Tytla is very much like Keaton in that his skills did not suddenly desert him, but the way his characters were conceived did. At Disney, Tytla animated several characters with a complex inner life. Grumpy starts off as a misogynist, but falls in love with Snow White. Dumbo goes from being a victim, persecuted for his appearance, before discovering his talents and finding the courage to exercise them. Stromboli is a supporting character and doesn't have much of a character arc, but he alternates between charm and threats, with explosive violence often rising to the surface.
Tytla left Disney to animate for Paul Terry. While Tytla did solidly crafted work in The Champion of Justice and Jeckyll and Hyde Cat, the conception of the characters is so limited that Tytla had nothing to work with. After leaving Disney, Tytla didn't do a single piece of animation that compares to his Disney work.
In live action, an actor gets to own a character. The actor can create a character's history in order to fill out whatever is in the script. As the actor will be the only person to portray the character, this allows the actor a major hand in conceiving who the character is and how the character should behave.
In animation, even when a studio casts animators by character, the animator is rarely the only one to inhabit the role. Usually, the animator will supervise a team in order to generate the necessary amount of footage. Even before the animator(s) get their hands on a character, there are many others who have a hand in shaping the performance. There may be a script. There will be a story team with different artists handling different segments of the film. There will be a voice actor who will interpret the script or boards in ways that will limit the animator's choices.
This level of fragmentation makes it more difficult to conceive a character as there are simply too many cooks. It is not easy to create a personality that an audience wants to spend time with. If it was, there would be more hit cartoon characters. Adding additional layers of history and inner life to a character is increasingly difficult when studio politics result in everyone wanting their point of view to dominate. Compromise, the inevitable result of politics, simply results in characters who fail to become individuals and instead are just a collection of traits.
Somebody with a deep understanding of character needs to drive the process. If it is a producer or director, that person has to be better than an actor in that he or she has to create the inner lives for all the characters, not just one. If it is left to the animators, they need more control so that the character isn't fatally compromised before it reaches them.
It can be done. In Toy Story, Buzz Lightyear sees a commercial that makes him realize that his view of himself is wholly false. That story point is powerful enough that the animators have something strong to work with. In The Incredibles, Bob is leaving for work and it appears to be a typical mundane morning departure. However, he is leaving on a mission that his wife doesn't know about (and wouldn't approve of) and he can't wait to get started. She believes that he is having an affair, so Bob's departure is more than leaving for work, it's the end of their marriage and their home. This is all conveyed through subtext. The dialogue says nothing of this.
The above are great scenes because of what's going on inside the characters' heads. A great performance can only come from scenes written consistently at this level. The acting starts with the writing.
In addition to the problems outlined above, there are others. Managements rarely admit ignorance, confusion or guilt. If things are going well, then management is obviously doing a good job. If things are going badly, then management "knows" what the problem is ("People must be tired of 2D animation. Yeah, that's it."). Artists often don't understand writing enough to supply what's needed for a performance at the story stage. Animators often get lost in the details ("it needs more eye darts") instead of dealing with larger character issues.
These problems exist regardless of what technique is used to animate a film. All of these issues contribute to the lack of great acting in recent animated features and in my opinion make it harder to create a great animated performance than a great one in live action. I don't know what the solution is, but I'd love to see people completely re-imagining the animation process with the goal of putting great acting at the center of it.