I bet WebSockets are much faster. So if I want to use lots of ajax continuously, WebSockets are recommended as an alternative?
I think is not a issue of speed, is a issue of comunication and real time process
Ajax is slower because the overhead. But Ajax is more compatible, Websocket is currently a bit experimental and it is not widely supported by most browser.
If you're in regular need of asynchronous data transmission I'd say you should try out websockets, it's really easy to use. One problem is - because of the early stage - the websocket interface might change (which has happended already) and render your web application unusable until you update your code.
It's two different technology things. With AJAX client just send request to server and wait to response. Websocket is HTML5 implementation for Comet technology, the idea is push information from server to client.