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By design logic-less templates force you to separate concerns thus helping you avoid future problems with refactoring. It also allow templates to be used with multiple programming languages without changes.
Pro Clean syntax
Mustache provides you with a clean and easy to understand syntax. Having a syntax that is readable is always a huge plus, since this means easier maintenance and code readability in the future.
Pro Available in lots of languages
Mustache is easy to deliver. If you need more features down the road, you can switch to handlebars, which is a superset of Mustache.
Pro Server side support
This would mean that you'll have a large community to help you out if you run into any problems.
Pro Can be compiled
Mustache templates can be compiled to JS files, so that they can be directly loaded.
Con Basic tasks are difficult
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.
Con Bested by Handlebars in many ways
Handlebars being an extension of Mustache bests it in both speed and power. It adds additional features to Mustache which make writing templates easier and faster.
Benchmarks have also shown that Precompiled Handlebars renders in about half the time of Mustache and the rewritten Handlebars (current version) is 5 to 7 times faster than Mustache.