RichFaces Ajax was created before JSF2 was released. In fact, originally, it was a separate product in its own right (a4j).
RichFaces Ajax has 2 benefits and 1 liability.
The benefits:
Works on older
JSF systems (1.2 and 1.1).
Simple to use.
The liability:
Requires RichFaces as an addition to the webapp. As opposed to JSF2's own AJAX, which is built in.
I haven't actually tried JSF2 AJAX yet, since all my currently-active projects have RichFaces in them. My impression is that JSF2 AJAX is clumsier to code, but since I have no practical experience in it, that may be a misconception. And considering all the options that RichFaces provides on its AJAX-supported tags, others may hold the exact opposite opinion.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.