One advantage to server-side rendering is that your clients don't have to use javascript in order for your pages to be functional. If you're relying on JQuery templates, you pretty much have to assume that your page won't have any content when rendered without javascript. For some people this is important.
As you say, I would prefer not to use the same rendering logic twice, since you run the risk of letting it get out of sync.
I generally prefer to just leverage partial views to generate most content server-side. Pages with straight HTML tend to render a bit faster than pages that have to be "built" after they've loaded, making the initial load a little speedier.
We've developed an event-based AJAX architecture for our application which allows us to generate a piece of content in response to the result of an action, and essentially send back any number of commands to the client-side code to say "Use the results of this rendered partial view to replace the element with ID 'X'", or "Open a new modal popup dialog with this as the content." This is beneficial because the server-side code can have a lot more control over the results of an AJAX request, without having to write client-side code to handle every contingency for every action.
On the other hand, putting the server in control like this means that the request has to return before the client-side knows what to do. If your view rendering was largely client-based, you could make something "happen" in the UI (like inserting the new comment where it goes) immediately, thereby improving the "perceived speed" of your site. Also, the internet connection is generally the real speed bottleneck of most websites, so just having less data (JSON) to send over the wire can often make things more speedy. So for elements that I want to respond very smoothly to user interaction, I often use client-side rendering.
In the past, search-engine optimization was a big issue here as well, as Jarrett Widman says. But my understanding is that most modern search engines are smart enough to evaluate the initial javascript for pages they visit, and figure out what the page would actually look like after it loads. Google even recommends the use of the "shebang" in your URLs to help them know how to index pages that are dynamically loaded by AJAX.
