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You could ask someone for translation of what I wrote earlier and what follows.
It's not an issue of stress, and it is not a matter of what is or isn't important at a given moment.
The choice seems to reflect the epistemic status of the denotatum. The of-phrase modification introduces a relationship as new. The genitive in "'s" relies on a presumably already known relation and is preferred whenever a more costly of-phrase would be functionally redundant and wordy.
Jacques-Louis David created a magnificent painting depicting the scene of suicide by Socrates.
It is appropriately titled "The Death of Socrates," and not "Socrates' Death."
"Socrates' Death," as an alternative title, would be hopeless.
However, in a paper about Socrates, I could write something like "After Socrates' death, his disciples remained in mourning for years."
Here, the denotatum—A, B, and the dynamic relation between A and B—is presupposed as established earlier and there is no need for its reintroduction.
To tease out this difference, one could be tempted to look for a hint in the grammatical realm of strong and weak definiteness: anaphoric definiteness is strong, and so is the definiteness determined by 's genitives. The of-phrased "the A of B's" are definite but weak; they gladly introduce novelties and not yet established relations.
The relation between Socrates (my colleague next door) and his desk is readily presupposed as well-established to the hearer when I say "I left the paperwork on Socrates' desk."
"I left the paperwork on the desk of Socrates" would be unacceptable.