"The Chief and the Didact; two different people, but are they really so different?
Context:
Eventually, the Didact managed to install some software that would allow the Librarian to effectively be with him, wherever he goes.
That's why the Librarian looks so small; it's her hologram.

Meanwhile, the Chief talks with Cortana.

The Similarities:
Chief and Didact are augmented warrior-servants of the highest rank (Master Chief Petty Officer; Spartan John 117, and Ur-Didact; Shadow-of-Sundered-Star respectively).
They both don't want to use Halo Rings to solve their problems.
They both had issues with their companions (Cortana/Librarian respectively).
Both are immune to a single Composer's output.
Both, in their times, would be called heroes, and eventually be classed as AWOL (Chief in Halo 5 / Didact when trying to stop the Flood on his own terms).
Both have comitted crimes they would regret in the name of the greater good (Chief killing Covenant, etc... / Didact composing humans to reinforce his anti-Flood war effort).
Both are strong in hand-to-hand combat, albeit never having actually engaged in such combat with eachother directly.

I would assume there may be more increasingly intricate similarities than these, but they are, for what I know, the basic similarities."