I am considering to put one of the following as a reference on my desk (as I am sick and tired to google every time I have a STL question):
I only have Josuttis's book The C++ Standard Library: A Tutorial and Reference, so I can't provide a comparison, but that book is very good, so I don't think you'd go wrong if you picked that. Also note that Josuttis covers the whole standard library whereas the other books seem to be only about the STL; that was the reason I got that book because I also wanted to understand things like I/O, which is not part of the STL.
All of Scott Meyers' books are excellent, including "Effective STL". It's not a handbook or a tutorial, but worth having.
I would go with the first - Josuttis' The C++ Standard Lib: Tutorial and Reference for the depth. I like to keep O'Reilly's STL Pocket Reference around for quick lookups.
I read The C++ Standard Library: A Tutorial and Reference, and found it extremely useful. I was already a "very advanced" C++ programmer before I read it, and I didn't feel like I was wasting my time reading through lots of beginner material.
If all you need is a reference reference, like what are the functions etc. you can try the SGI STL reference documentation. Granted, it's not a book, and it is a bit dated, but it's fairly well done, and has good documentation of concepts etc.
Just my two cents!