Bothe of these phrases seem to express and depict the same meaning.
As I can remember, John was kind-hearted and tolerant; let alone, he was a man of God.
As I can remember, John was Kind-hearted and tolerant; not to mention, he was a man of God.
How to use and differentiate between them?
not to mention:
In addition to or as well as what's been discussed; used for adding a comment that emphasizes the main idea of what you have already said.
used for saying that something is even less likely to happen than another unlikely thing; used to emphasize that something is more impossible than another thing: