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.