Both terms are perfectly acceptable in the cited context. Broadly speaking they mean about the same thing - it's just that they have significantly different connotations.
Native speakers will understand this specific use of growing as a metaphorical reference to developing, improving (intellectually and/or emotionally, not literally as in increased physical stature). Even a 70-year-old could say something like...
I still like to learn new things - when you stop learning, you stop growing.
In the above context it would be extremely unusual (bordering on "nonsensical") to use growing up, with all its connotations of the specific difference between childish and adult behaviour / attitudes.
Note that to grow up in this context is similar to to end up, to finish up, to break up - that added preposition imparts a note of "completeness, finality". The implication being that there are only two possible states for a human being - childish (but "developing") and grown-up (a static end state).
TL;DR: If you want to talk about how people (young and old alike) can develop / improve their emotional and cognitive skills by continually exposing themselves to new experiences and information, use growing.
If you just want to focus on (one of) the defining characteristics of adolescence (the transition from child to adult), use growing up.