Can we use both? Or may we be better off - from an SF perspective - with neither?
The words themselves have been wrested from everyday use into a new world of specialist jargon.
Competent used to mean good enough to do something. So a competence (the noun) gets to be seen as a kind of ability, often indicated by a certificate.
Strong conjured up physical strength mostly, was a special, outstanding quality, which had to impress people before it got mentioned. Strength also is a noun, and there’s a danger of looking for things (nouns) as somehow residing inside people, losing the context of where they are doing stuff.
Now in the professional, career coaching sphere, the terms are contested. Even the spelling is up for grabs - competences or competencies?
A ’strength’ becomes something you are good at, and you feel energised to use them. But strengths can be over-used or over-done, and suddenly become a weakness. (How can that be possible?)
Strengths are more about individuals and what they can do. Competencies are put together in frameworks to show what organisations need from people for them to serve in particular roles. They can offer a list, for example, of desirable leadership behaviours. And they can be constraining for recruiters and exclusionary for applicants.
In solution-focused circles, we are more interested in resources - whatever might prove useful for you or your team - in a particular context. Those resources aren’t necessarily psychological constructs (like ‘strengths’), so much as experiences, skills and your connections (inside and outside the team). And interviewers can discover these in plain, non-technical language, with more clarity, more fairness, less cost and less bureaucracy.