In Space Seed Khan had a fight with Kirk but admittedly it was rather Montalban's muscles and body language which created the impression of a physically superior and aggressive human.
In TWOK he appeared more like a conventional master who commands his minions. While he does some of the sadistically pleasurable work (the Ceti eels) in general he just pulls the strings.
In STID he is on his own which is precisely why the Khan vibes are missing a bit. The guy is not a superhero movie kind of lonesome psychopath (Cumberbatch is great in playing him as this!) but a ruler and thus a social creature; he is interesting precisely when he interacts with other people, charms them and makes them follow him willingly (Space Seed would not work without McGivers) respectively subjugates them.
When Khan goes crazy in TWOK he somehow becomes ridiculous. It's kinda like with a stern father, his authority rests on his demeanour, his piercing look and so on, i.e. more on the threat than the execution. When he loses his temper and hits you it does of course hurt but he also does become to some degree impotent. You can perceive this loss of authority in TWOK when Joachim questions Khan, it is clear that he is only following him because he perceives him as a boss who gives commands and not as a leader who knows best anymore.
And I think this is why Khan doesn't feel a 100% like Khan in STID, he is in crazy revenge mode ever since Marcus tricked him. While we do see his calculating side for some time we never see Khan the former ruler of a quarter of the Earth, Khan the political creature.
TWOK is a great movie not because of but in spite of Khan. The character has his best moments in Space Seed so repeating patterns from TWOK ad infinitum without actually thinking about them is bound to fail. And lest I am misunderstood, I like Cumberbatch's villain but not the name of the villain.