Which will scale best for performance, file-size, (and my sanity): Animated .gif
s or a spritesheet with animations using CSS (and JS when need be)?
Animated gifs only give you binary transparency (a pixel is transparent or totally opaque). That's why most animated gifs look bad on transparent backgrounds because you cannot apply antialiasing (like your squirrel, some antialiasing there would do wonders).
If you want to have PNG-24 transparency quality you have to go with animated sprites.
Also, animaged sprites performs really well if you draw them on a canvas. Look this: http://seb.ly/demos/bunnybench/bunnies_canvas.html