its depends only clients requirements because in according to my experience a good web designer don't face any problem in both type of layout. i have design many website some is fixed bases and some is fluid and i don't realize anything different both of them according to my experience, just a little bit difference is a fixed width thats it. you can see my personally portfolio on my website.
I would have to go with the fixed layout, it's what I normally use, because I only know basic html. I don't know how to make anything really fancy. I really don't know the differences between the two, maybe someone here will say something about it. I only know that one takes more coding than another, but would probably have to see an example of the two so that I would know the difference.