I've never used Boost.Functional, only briefly read its documentation. Looks like it's an improvement to Standard <functional> header.
An example on the main page of Boost.Functional (Usage section) was chosen as an introduction to the library. The same can be done easier using Boost.Bind (or Boost.Lambda). Also, Boost.Bind is an excellent alternative to other tools from <functional> header.
I'm curious, is there anything from Boost.Functional or STL <functional> header that cannot be done by Boost.Bind? Or any other benefits of Boost.Functional?