We also tried answering it, when we realized that our client-side architecture was mixing DOM manipulation with application logic. This is not surprising for developers that use jQuery in the old fashioned way, as it seems that jQuery actually encourages that kind of behavior because of its syntax and the simplicity of using it.
So which part do we really want to test? This depends on what’s more important for you to verify in your application. One thing we agreed on: we need to separate the client side code into layers in order to make it testable. One layer will be pure application data logic, and the other one will be a wrapper to the code that actually manipulates the DOM (first one uses the latter).