Unless the PrimeFaces and RichFaces teams explicitly say so, I'd be very reluctant to mix PF and RF even in the same
application, much less on the same page.
There are some extension tagsets that can be mixed and matched with impunity, but the more complex ones often do their magic by tapping deep into
JSF's internal operations and sometimes they both want to tap the same resource, but do so in conflicting ways. Periodically, JSF adds improvements designed to minimize the need to do this sort of stuff (or at least co-ordinate it), but it's a bit of a gamble if no one is willing to certify it.
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.