Can someone please explain to me in terms that even I can understand when a GM would prefer one over the other when calling for Initiative checks? It seems to me that these two skills and their usage for this purpose has the potential to confuse and perhaps be the subject of much debate at the gaming table.

Cool - "I know there is an attack coming, this is obviously a hostile situation" (people in the room are brandishing weapons)
"I am trying to ambush this guy"
"I am initiating the fight"

Vigilance - "I am constantly mindful of a possible attack, but this situation is not-obviously hostile" (nobody has weapons drawn)
"I have been surprised"
"I was not expecting combat when I walked into this room"

I actually kinda like the idea, or at least, I like that each skill provides a useful benefit (cool is based around having that perfect timing, while vigilance is basically the boy scout skilled with its "always prepared" use).

KommissarK said:

+1 -- you got it, Kommissar!

It also permits the ability to have Force-users who have the classic "Jedi Reflexes" and thus react to danger rapidly (bonuses to Vigilance checks via the Uncanny Reactions talent) but aren't any better when they already know violence is eminent (no such boosts to Cool checks).

Thank you very much for the distinctions made through example. That helps clear things up a bit.