The component a4j:outputPanel offers the attribute ajaxRendered which should update the contents of the panel at every ajax request (see Chapter 2 of the Component Reference). But on a small testpage which is attached, this can easily be disproved.
When using the first spinner of the example (which uses f:ajax), the new value gets submitted into the model, but the outputPanel is not rerendered. If I use the second one (with the a4j:ajax inside), everything works as expected.
This effect is the same e.g. for a4j:commandButton vs. h:commandButton + f:ajax and other constellations.
I would expect (especially when reading the reference) that the panel is rerendered even in the f:ajax case.
Additional note: In contrast to this, the status-indicator works for all ajax requests, nevertheless if it is raised by an RichFaces component or f:ajax.