I feel like you can sort of break down the performance into four categories of exponentially decreasing importance: the body, then the eyes, then the face, then the lip-sync.
Most animators would agree that the body language and pantomime is by far the most important aspect of the overall acting performance in a medium shot or wider. (i.e. not a close up on the face). Unless we are face to face with someone, the body is the first place we unconsciously read in order to communicate with someone. Why? I'm not sure, but it might be because our body language often betrays our true feelings, our true mood or personality, our true intentions and desires, etc. When we consider that, it isn't surprising that we would pay at least some amount of attention to the body language of the person we are approaching.
In short, if you can get the emotions and ideas to read in the body, then the audience is going to understand what's going on and feel those emotions.
Next on our list of descending importance is the eyes. If the body is 90% of the acting performance, the eyes are 90% of the facial performance. After considering what the body will be doing, the next most important thing is definitely your eye performance. As always, the most important (and sadly, the most often skipped) aspect of doing eye animation is to know WHY you are animating the eyes. I see a lot of demo reels with randomly floaty eyeballs, and it can really kill a performance. Know exactly when and how and (most importantly) why you are going to move the eyes before you dive into your animation. Blinks go along with this, and are just as important for communicating thought process and emotion, and in certain instances I'd include the brows in this category as well.
After the eyes, we've got the overall facial expressions, including mouth emotions (smiles, hanging jaw, frowns, etc).
Obviously the eyes are a part of a facial expression, and the whole face should be thought of as one cohesive unit, but for the sake of this talk, we can think about it as a separate entity -- only because the rest of the face, while very important to the overall communication of the character, is simply not quite as important as the eyes themselves. If you animate a great body performance with great eye animation, that performance is going to read perfectly, regardless of whether or not you have a full facial rig to work with. This shows the importance of the eyes over the rest of the face, but that's not to say that you shouldn't take great care in the creation and choice of your facial expressions.
Last, and certainly least, is the lip-sync. Great body acting paired up with expressive and alive eyes, combined with well-timed facial expressions -- that combination is going to look terrific, even without the lip-sync. This is why you'll hear a lot of people say that lip-sync is the icing on the cake of the overall animation. It's that last extra little bit of "wow" you can add to your scene, and by far the least important aspect of your acting performance.
None of this is to say that any of these four categories are unimportant, some are just more important than others. Really terrible lip sync will certainly ruin a shot on a demo reel, but my point is that mediocre lip sync combined with otherwise great animation will probably go unnoticed, and the recruiter will be left with a feeling that the overall shot was great, even though the lip-sync itself might not have been fantastic.
So, I guess as far as which is the icing on the cake, it sounds like the eyes are the icing on the body language cake, the facial expressions are the icing on the eyes, and the lip-sync is the icing on the face.
In vaguely related news, I love cake but really dislike frosting/icing, which my wife thinks is completely insane, but she doesn't mind as it leaves more icing for her...
Thanks for reading, and thanks for the great question Fernando!