Is the server or the client in control?
It depends. With AJAX the answer is more in between. Control can be more centralized in a server-side component or as a mix of client-side and server-side controllers.
There are some use cases where an entire AJAX application can be written in a single page. Keep in mind if you choose this type of architecture that navigation and bookmarking should be considered. Both methods are viable depending on what you are trying to accomplish. I tend to prefer spreading the control across the client and server.