Here is the link to the original post by Sarah Drasner titled A Comparison of Animation Technologies. It's a great post that goes through some history of the subject as well, but if you want a "just the facts" answer to the question it basically boils down to this:
Use css for basic animation, greensock's TimelineLite for chaining animations, and a framework (like Three.js) based on webgl for 3d. :)
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