You should be using Illustrator to design logos, yes, but Fireworks and Illustrator are both deficient to Photoshop for designing web layouts.
This isn't to say that you can't use Fireworks to make a good layout, but you just have more freedom with Photoshop. FW obviously makes it easier to go from design to code, if that's what interests you the most.
This is an age-old disagreement between people who are more familiar with Photoshop and those who are more familiar with Illustrator. Usually, it is paired with a certain ignorance on the Photoshop side (due to a lack of better knowledge), whereas the vector people know that these folks simply don't know how to handle Illustrator correctly.
"You have more freedom with Photoshop" is an ignorant statement to make. You're either picking up on cliches or you don't know how to use Illustrator.
Illustrator is quicker and far more flexible for object based designs - which every website is by nature. As is Illustrator.
Fireworks is a combination between the two, but some people are not as familiar with it (yet) since Adobe bought Macromedia not that long ago. Photoshop is a raster graphics manipulation application and doesn't come with the flexibility or functionality of an object oriented program such as Illustrator, because it was never meant to have that purpose.
PS is far more popular though because it is a good all-in-one tool. It has a flatter learning curve than e.g. AI. But it is not the most professional choice by far. Some people even call it the web design tool of wannabes and semi-pros.
It's up to the individual to find out what works best for you anyway. If it is PS, sure - you will find an abundance of web design tutorials for it on the web. You
can make a decent looking web design in a raster program. If it's AI or FW, thats fine too, plus you know that you're not alone, since almost every professional and agency I know and have worked with uses these tools. You will find less beginner tutorials on these two though.
