Why is a larger sensor important?
How much better is a full frame sensor at 16mp vs a APS-C at 16mp?
What about a full frame at 10mp vs an APS-C at 16mp?
While you may get a hand full of technical answers that mention many differences etc etc,
Full Frame is not better so to speak - but different. Depends on what you intend to shoot.
Now a quick answer based on looking through the viewfinder from a photographer "in hand standpoint" the only way to really get the idea is to use the same lens on a crop body and then on a full frame. I'm talking about the difference in image size/shape (magnification) only here.