I've always played with the idea that while Denethor consistently favored Boromir out of politic necessity (Boromir was the heir and would have to take over,) and out of a certain emotional apathy arising from his despair, Faramir was really his favorite all along, although Denethor would never have admitted that to a living soul. Their minds and souls were very much akin as highly insigtful & intelligent Numenoreans, whereas Boromir and Denethor had nothing in common-- leading Denethor to be protective of Boromir, and perhaps too indulgent, hoping he would grow into the Stewardship.
Consider Denethor's bitter jealousy of the friendship of Faramir & Gandalf. Denethor has many reasons to be suspicious of Gandalf, but the degree of jealousy suggests a real longing for exclusive possession of his son's love-- more in line with Faramir being his real favorite and Denethor feeling rejected.
After news of Boromir's death came, it might have been easier for Denethor to believe that he ironically sent his favorite to his death-- a cruel twist of fate, but with no possiblility of guilty choice on Denethor's part. The deeper fear would be that Denthor indeed made a choice, choosing death for his less loved son and relative safety for his more loved son-- that he sacrificed loyal Boromir to save Faramir, that ungrateful Wizard's thrall who never really loved his old dad as he ought.
Of course, at the time, Denethor actually made no choice at all, as he did not expect the quest to be fatal-- but he might well have wondered later if he had made a choice without fully knowing it, considering that the foresight of the Numenoreans made this possible. (See Halbarad, Aragorn)
Although I think Boromir is the better captain in battle, being as brave, stronger & more cheerful, Faramir's my favorite, as he is the better strategist and general, and almost as good a captain. I think Denethor preferred Faramir also.
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