I constantly hear people use the word "resiliency" (especially sports broadcasters and the like). I've always used "resilience" instead. Is there a preferred word to use in any given situation?
As far as I can gather they are exact synonyms.
Resiliency is just a variant of resilience. Which one is used is a matter of style and personal preference. I would always use resilience because it's one syllable shorter than resiliency. Others may have different opinions. It doesn't matter because they are, as you suggest, exact synonyms, except for the pretentiousness of the longer word: resiliency. All verbosity is pretentious.