Question: I have moved into a house with a nice Wolf-range griddle, and I would like to know what the primary advantages of the griddle are over a cast-iron skillet, including, is there anything I can do with a griddle that can not be done with a skillet?

I have found that the primary downside to using the griddle is the time it takes to heat up, so when cooking for one, I would choose the skillet. The primary advantage of the griddle is that it provides a larger, easier cooking space. 

Am I missing other major advantages of having a griddle?

Answer: 
Surface area is the biggest difference. You can do a much larger job on a griddle than in a skillet. Even 2 or 3 jobs at time, and when you are done there is just the griddle to clean and not several items. 

You will also want to pick up a '[bacon press](http://rads.stackoverflow.com/amzn/click/B00004UE7B)' to minimize splatter when you put bacon on your griddle.
I'm going to just use to frying pans ('skillets'). The lack of sides allows stuff to fall off too easily - I fried chopped onions today - and there's no carrying handle - so you can't move the griddle to plate up. The other downer - my griddle's cast iron and it's just cracked while heating it !