In the "Siren Song" there are three Sirens and in the "Odyssey" there are only two sirens. The Sirens in the "Odyssey" sing a song filled with passion and yearning to lure men to them. The Sirens in "Sirens Song" use a song of secrets to lure the men treacherously to their deaths.
The "Sirens Song" Sirens use the mens own natural curiosity to bring the men to them. The "Odyssey" Sirens use enchantment and the promise of passion to get the men.
I believe that Ms. Atwood did not want the Sirens in "Siren Song" to be the stereotypical siren of mythology. They are smarter and more deadly than the ones in the "Odyssey. She seems to be saying females don't always have to use sex to interest a man and that makes them totally different and modern.
The Sirens in the "Odyssey" use the promise of sex and the enchantment of their song to lure men to death. The passion in their voices held such a strong hold on the men that they could not turn away.
If you did not know that the "Odyssey" was written by a man you could more than likely tell by just the part about the Sirens. Women causing the troubles of man seems to be the theme throughout the ages for male writers.
Ms. Atwood talks about the sirens from a totally different viewpoint. You would know that "Siren Song" was written by a woman from the tone of the poem. She could be saying that men are easily led by their desires, but their curiosity is an even more powerful tool to be used by a crafty female.