I've been using Devise for a little while, and I've realized it's built on something else called Warden that handles authentication. What does Devise offer me outside of Warden, because I was considering removing devise and just using Warden.
Warden is the kernel of rack-middleware authentication. Devise is a complete authentication system for rails applications.
Let's take an analogy: Warden is like the Linux kernel, while Devise is like a complete Linux-based operating system such as Debian or Fedora. Or another: Warden is like the engine, while Devise is like the rest of the car.
For more details, please read the respective manuals that you linked to in your question.