When working with templates it's extremely important to understand the HTML elements at play, and to see them as natively as possible. Jade removes this, making developers have to do the abstraction in their heads.
The structure is entirely determined by the indentation. That means that indentation errors will ruin the end result, often without an easy way to find the error. Indentation errors are easily introduced by copy-pasting, by rearranging code and by working in a team where not everyone uses the same...
Mustache js's attempts at making some things simple makes them so easy that they're almost difficult. That is the case with some basic tasks like figuring out how to apply css to shade odd/even rows on your template based content.
Vue can easily be integrated with other front-end libraries. This makes it an extremely versatile tool. It's easy to fix its shortcomings or compensate for missing features by just plugging in another library.
Since the number of people currently using Dust.js is quite insignificant as compared to Mustache js and Handlebars, you're less likely to get your question answered or issue resolved if you start using it.
React can render it's components and data server side, then it sends those components as HTML to the browser. This ensures faster initial loading time and SEO friendliness out of the box, since it's indexed as any other static website by search engines.
React's virtual DOM is fast, but it requires storing elements in the virtual and real DOM increasing memory usage for the page. This can be a real problem for single-page webapps designed to be left running in the background.
One of the best features of squirrelly is that you can pass in options to the content of script tags (for example, as variables,) and carry out advanced logic there. This is also a great way to transmit data between client scripts and the server.