I've used an expression "core competency" for years and recently found out that it is correct to say "core competence", as in "growing vegetables is my core competence". Now I'm in doubt so I'm asking here. What is the right way to say about what I'm most competent at?
Both words are in the OED, with almost identical definitions (except that competence has a couple of specialised meanings that competency hasn't).
An ngram of the words shows that competency was slightly more common than competence until about 1890, but after 1920 the prevalence of competence rose rapidly: today it is about six times as common in books as competency.
An ngram of the phrases shows that core competence/competency were almost unknown until 1990, since when they have both risen rapidly, with core competence about 50% more common than core competency.
On the other hand, GloWbE (the corpus of Global Web-based English) has core competency more common than core competence (40 instances against 27); but competence three and a half times as common as competency (6840 against 1987).
So, both are acceptable, in general competence is rather more common than competency, but in the comparatively small number with core, the different corpora disagree as to which is more common.