Similar questions have been asked before and they all reached the conclusion that AJAX will not become obsolete. But in what ways is ajax better than websockets?
Wit
Personally, I think that websockets will be used more and more in web applications instead of AJAX. They are not well suited to web sites where caching and SEO are of greater concern, but they will do wonders for webapps.
Projects such as DNode and socketstream help to remove the complexity and enable simple RPC-style coding. This means your client code just calls a function on the server, passing whatever data to that function it wants. And the server can call a function on the client and pass it data as well. You don't need to concern yourself with the nitty gritties of TCP.
Furthermore, there is a lot of overhead with AJAX calls. For instance, a connection needs to be established and HTTP headers (cookies, etc.) are passed with every request. Websockets eliminate much of that. Some say that websockets are more wasteful, and perhaps they are right. But I'm not convinced that the difference is really that substantial.
I answered another related question in detail, including many links to related resources. You might check it out:
websocket api to replace rest api?