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.
Works on older JSF systems (1.2 and 1.1).
Simple to use.
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.
An IDE is no substitute for an Intelligent Developer.