During the final fight sequence between Spock and Khan. Spock applies the Vulcan nerve pinch to Khan, who lets out a scream of pain but doesn't collapse.
Why didn't the nerve pinch work?
In the original series "Assignment: Earth", the human derived from a hidden planet, Gary Seven, shrugs off a Vulcan nerve pinch without any discomfort at all.
Khan is not incapacitated by it, but does create much pain for him—so presumably it would be worse for anyone else. We don't know if his superior muscularity guards the nerves or if his genetically engineered nervous system is better able to cope with the paralysis effects normal to humans.
Presumably then, the maneuver is most effective on more weakly engineered humans. The most advanced are less affected by it.
Spock's Vulcan Nerve Pinch was much less effective on Khan, due to his superior genetic engineering. Although, it had a temporary painful effect, Khan, as stated in the film, was the most dangerous adversary they have/had ever faced.
It makes sense that in Khan's world, genetially enhanced humans are placed in a meritocracy, the most perfect (i.e. him) at the top, and less enhanced people in lower ranking positions. Therefore, it is perfectly possible that the engineered human who goes down instantly in Space Seed is one of these less-enhanced people, maybe only with enhanced mental capabilities (like Bashir in DS9)?
Khan has been engineered to a level of physical perfection well beyond normal humans, and presumably even beyond many of the alien species, so it's only logical that his neuromusculature is more resistant to an attack such as the Vulcan nerve pinch than other people's.