I have not read Mandelbrot's book (yet!), so I can't really compare it.
I don't know what sort of depth you're looking for, but I'd call CBoN a "medium"-depth book on the subjects involved. It's possible to read it like a pop-science book and still appreciate it, but you can actually sit down with pencil and paper (or write some code) and gain a pretty good level of insight. You're not going to necessarily gain a complete understanding of all the underlying math, though, just by reading this book.
Anyway, it's a pretty darn good use of $40, IMO. Buy it!
The Mandelbrot book was the first one on the topic (published in 1983, revised from books published in 1975 and 1977), and is the least likely to have 'recent information on the topic'. It's also not as readable as some of the others, but it's certainly a classic (and deserving of a larger Wikipedia article than it currently has).
have you read that book and would you recommend it over "The Fractal Geometry of Nature by Benoit Mandelbrot (1982) [1]?
I'm asking because I bought the latter and would like to know if this book provides more recent information on the topic.
Thank you.
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[1] http://www.amazon.com/Fractal-Geometry-Nature-Benoit-Mandelb...