c:if is probably not the best way to do whatever exactly you want to do. In fact, it's better to not use the JSTL tag libraries in JSF at all (certainly not if you are using a newer JSF version).
Why not bind the value of the selectOneRadio component to a property of one of your beans:
That way, whenever the page is submitted, the 'someProperty' property of bean 'myBean' will automatically be set to the selected radio button value ("ABC" or "XYZ"). If you need more logic, you can put that in your Java code in beans instead of in your Facelets pages. Beans are the right place to program business logic.