I've read "American Gods" and "Anansi Boys" and preferred the latter. I just liked the characters better and story was less muddled. "Neverwhere" was also a fun read but less engrossing.
I enjoyed
American Gods a lot. In fact, I'm currently halfway through my 2nd reading of it, and I almost never reread novels. It just felt right to start a 2nd reading of it when I embarked my own cross country road trip a couple months ago. I think Shadow is a very compelling protagonist. I found his relationship with his wife very real and heartbreaking. And I love some of the supporting characters that populate the story, like Mr. Wednesday, Czernobog, Mad Sweeney, & Anansi.
I loved
Anansi Boys even more. His style of comedy reminds me of the late, great Douglas Adams (moreso his
Dirk Gently books than his
Hitchhiker's books).
Neverwhere I gave up on halfway through. While it demonstrated as much care in its worldbuilding as the other books, the prose was much weaker. I guess that's not surprising since it was his first novel, therefore far less polished than his later works like
Anansi Boys.
It was while reading
Neverwhere that I realized that many of Neil Gaiman's novels are essentially the same story, using the exact same template as Douglas Adams'
The Hitchhiker's Guide to the Galaxy. A meek, mild mannered British man is inadvertantly pulled into a bizarre new world populated with strange people & creatures that he is unable to comprehend. This same template is used for
Anansi Boys, Neverwhere, &
Stardust. American Gods shakes things up a little bit by using the same story but giving all of the characters a distinctly American feel. I guarantee you Shadow would intimidate the hell out of Fat Charlie Nancy, Richard Mayhew, Tristran, or Arthur Dent.
The main difference between
The Hitchhiker's Guide to the Galaxy & Neil Gaiman's work is that all of Gaiman's characters also have some kind of preexisting girlfriend issues. Tristran wastes his time trying to impress the stuck up popular girl. Richard Mayhew has a frigid bitch of a fiancee. Fat Charlie Nancy's girlfriend steadfastly refuses to put out. Shadow's dead wife cheated on him with his best friend. I'm starting to suspect that Neil Gaiman has issues (similar to Russell T. Davies' issues with parents on
Doctor Who).
Nobody has succeeded in spelling "Anansi" yet.
A few have but, you're right, too many have either misspelled it or mistakenly think it's "
Anasazi Boys." It's not. It's
"Anansi." Anansi is the African mischief god who fathered the 2 main characters in
Anansi Boys. Anasazi is an old Native American tribe from Arizona. They have nothing to do with the works of Neil Gaiman so far as I can tell.