Scylla and Charybdis are two sea monsters of Greek mythology noted by Homer. Later Greek tradition sited them on opposite sides of the Strait of Messina between Sicily and the mainland of southern Italy. They were said to be located close enough to each other that they posed an inescapable threat to passing sailors. Avoiding Charybdis meant passing too closely to Scylla, and vice versa.
Scylla was said to be a creature who was rooted to one spot in the ocean, and regularly ate sailors who passed by too closely. She was described by Homer in The Odyssey as having six heads perched on long necks along with twelve feet. In Ovid's Metamorphoses, she was depicted as having the upper body of a nymph, with her mid section composed of dog's heads. Charybdis was depicted with a single gaping mouth that sucked in huge quantities of water, and belched them out three times a day, creating whirlpools.
According to myth, Odysseus was forced to choose which monster to confront while passing through the strait. He chose to pass by Scylla and lose only a few sailors, rather than risk the loss of his entire ship into the whirlpool. Jason and the Argonauts were able to navigate through without incident, with Hera's assistance. Aeneas was able to bypass the deadly strait altogether.
[Thank you, Wikipedia.]
Incidentally, JoeRay, I think you referenced this myth in answer to another question, which I found after your added detail above. It is true that a "Scylla and Charybdis" connection can be made to several modern sayings ...
~ I am caught "between a rock and a hard place."
~ It seems you are "damned if you do, damned if you don't."
~ Now we are stuck "between the devil and the deep blue sea."
An example using your phrase ...
~ For Yahoo, choosing between Microsoft and Google must seem like "sailing between Scylla and Charybdis."