There is a case for doing both, pre-rendering on the server, and rendering updates on the client. This approach is used by Google plus for example.

I wrote a simple implementation that uses google closure templates to pre-render the page with dynamic content on the server, and to me the app felt more stable. This feeling may be entirely subjective, as I didn't make any actualy measurements.

A counterargument may be that this approach does not scale and would overload a server resulting in worse stabilit/render-time in the end.