There’s a short article here on how they modeled the birds in Plumiferos. Mostly, the feathers were mesh modeled individually. My guess is that the Pixar birds’ feathers are likewise modeled individually. Takes a bit of time, but if you really want the best possible results, which can be animated and deformed exactly how you want them to be, this is probably the solution.
Fur is not the same thing as feathers like this ones
A pretty convincing feather effect is possible with particles, as you can see in the picture, in the one marked “feathers”.
You could use a combination approach with different methods for different kinds of feathers on your character.
The dupliverts solution looks like it’s got some potential but I wonder how it will be to animate over an entire bird.
Maybe Blender is still really amateur and incapable of doing these kind of CG technics.
That’s probably not the problem here. In any case, to get professional results like this requires a lot of effort no matter what software you’re using.