The relationship between the hero of fiction and the villain is, by its very nature, a vexed one.
The archetype, of course, is the rapport between Sherlock Holmes and Professor James Moriarty. A faithful rendition of the original meeting as described by Conan Doyle has elements of esteem mixed with profound enmity:
A more modern adaptation of the same scene:
I like how Gatiss uses the old lines ironically, and how the scene performs a similar function to Doyle's, but in an entirely different way.
Of course, in the new series, the Doctor and the Master take this to an extreme…