Should I fill my pool up with water or drain it for the winter?

I live in Chicago, Illinois and I have a in-ground pool in my backyard. You know how cold the winters get here. I have asked several people on advice on what to do with it in the winter. Some say I should fill it up with water and just leave it open, while others say I should drain it out and cover it with a protective winter cover. What should I do? And why would that be better over the other alternative?