Illustrator is the real deal. This is the tool professionals use and it is far more powerful than Fireworks. If you are just learning, learn with Illustrator.

That said, I use them both often and sometimes together. I use Fireworks when creating simple art for presentations or interface prototyping. It is a fast, easy and for me, very familiar. I can crank out a quick set of shapes, make some quick improvements to an image, etc.

I use Illustrator for my more fine honed work and when I want a more powerful set of filters and drawing tools.

Hope that helps.