The Idea: Cyborgs plan to extract emotion to turn the entire human race into them; often, converted Cybermen can still remember who they once were. The Daleks were based on the Nazis, that's common knowledge. With the same evil ideology, they terrified audiences that only seen these things twenty years before; they were an image of the recent past, both familiar and alien. The Cybermen though are an image of the near future; just as scary, with just as evil an ideology. What's so terrifying about the Cybermen is that they are us, but what's absolutely nightmarish, is that often, they remember the people they used to be; a converted Yvonne Hartman cried a single oily tear, knowing that she'd done her duty, and when inspecting a Cyberman in Pete's World, the Doctor found out that it was a woman about to get married in the morning. These examples aren't just horribly sad, they reinforce the idea that these creatures used to be human; sure they look humanoid, but aren't they veering further and further into the future, with crazier technology with every new upgrade? That's why Neil Gaiman's 'Nightmare In Silver' missed the mark: they didn't feel like Cybermen, they just felt like robots. The beauty of Cybermen is that they're from the near-future, the same as Daleks resonate with the near-past. If you really want to scare, hit as closest to home as possible.
