There is no one answer to this, it depends on the application. AJAX is basically Asynchronous Javascript And XML. So, it is a platform, or philosophy of programming. With AJAX you can update ELEMENTS of your page without having to reload the entire page. The math here is simple in terms of bytes transferred per click.
For example, with AJAX you can dynamically check user input as s/he types something into a form input box. See this feature on answers.com, where each letter you add narrows down the available terms in the database which is shown in a drop-down box. This is fast and clean way to suggest alternatives to what you search. Without it, you would have to type in entire word, or parts of it and entire page would have to be reloaded in order to suggest you alternatives. With a page with many elements and lots of images, it may become cumbersome and annoying to load entire page for such minimal updates.
On the other hand, any content created with AJAX does not have, by default, a fixed URL since it is obtained client-side with Javascript. This is most often mentioned as major drawback of AJAX, but it also depends on the application. Using AJAX to navigate a site is clearly not the best choice since the navigation is then client-side with no fixed URL. Using AJAX to check input before submission or to dynamically load parts of page that need asynchronous update is by all means effective.
