I am creating a new MVC4 project, and research has lead me to believe that communicating from javascript to the server side is better achieved now through web API framework
Even if your project is so complex as to warrant two "front ends" then I would still only consider splitting out webapi into a separate project as a last resort. You will have deployment headaches and it would be difficult for a newbie to understand the structure of your solution. Not to mention routing issues.
I would aim to keep the system.web namespace isolated in the one "presentation layer". Despite the webapi not being presentational it is still part of the interface of your application. As long as you keep the logic in your domain and not your controllers you should not run into too many problems. Also, don't forget to make use of Areas.