Difference between the use of "resilience" and "resiliency"
Solution 1:
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.
Solution 2:
Resilience is the more accepted form in the USA.
[I]n today’s English, resilience is far more common than resiliency, especially outside the U.S. and Canada. In North American publications, resilience appears about four times as often as resiliency. Outside North America, resiliency appears only rarely.
Though resilience is more common, resiliency is not incorrect. Both words are around five centuries old, and it wasn’t until the late 19th century that resilience prevailed by a significant margin. Still, there’s no reason not to use the shorter, more common form. - Grammarist
Solution 3:
My opinion is that "resilience" is the CORRECT usage. Americans especially seem to like adding syllables for some unknown reason. Maybe to sound smarter?