One would hope that Boost continues to support existing classes, for a couple of reasons.
First, there is a body of code that uses the overlapping features in Boost that needs to be supported, for some time.
Second, overlapping implementations allow me to select which one I'd prefer to use. There might be some difference between std::Frob and Boost::Frob that is important to my project, and having a choice is good.
In the long term, though, I would expect a migration toward the standard from both the application writers and the tools providers. That makes it a less risky choice to go with std::.