The Faramir similarity comes primarily from the Numenor/Atlantis dream, referenced in Letter 163:
Quote:
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I say this about the 'heart', for I have what some might call an Atlantis complex. Possibly inherited, though my parents died too young for me to know such things about them, and too young to transfer such things by words. Inherited from me (I suppose) by one only of my children, though I did not know that about my son until recently, and he did not know it about me. I mean the terrible recurrent dream (beginning with memory) of the Great Wave, towering up, and coming in ineluctably over the trees and green fields. (I bequeathed it to Faramir.) I don't think I have had it since I wrote the 'Downfall of Númenor' as the last of the legends of the First and Second Age.
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There may have been other personality-similarities, but I'm not personally aware of such, and in any event this is the one that most people will know of.