I've worked with both Ember.js and ExtJS / Sencha on front-end projects with close to 100k lines of JavaScript code several years ago. JavaScript was the problem in both (developer written JS), stuff would sometimes work in one browser and not 100% in another browser (minor things, but in the corporate world, minor errors could cost you your contract),
Less files we had to manually build a build script for, we had issues where we had to tweak our code to make minification work (In Dart that's taken care of for you). We had over 5000 selenium tests running over and over the whole day and javascript errors which could have been avoided with a stricter type system went unnoticed often.
The components are nice, if you can replace the JavaScript with Dart, it'll be an excellent choice.