Although we do still use the expression "faint-hearted", Brits don't tend to say either "brave at heart" or "strong at heart" these days. We just say "brave" or "strong". You may find references to "stout-hearted" (ie brave) people in literature, but it's rarely used nowadays.
If someone were about to start watching a ghost/horror film, I might say "Don't be scared! [It's not real!]" If a child were about to have an injection or go to the dentist (or something similar), I might say "Be brave".
I can't think of a situation in normal, everyday, modern English in which I would use "brave/strong at heart".
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