Since dart will have to compile down to javascript for any browser that isn't chrome* , there probably wont be much, if any, performance improvement that you can depend on. Your only way to be able to use the speed up would be to restrict your client base to chrome only users. With that said, regular old javascript is really a much more interesting language by itself than dart. Perhaps I'm opinionated, but I just don't see anything exciting about Dart.
* This is based on most browser vendors not being supportive of it.