I think that a small tragic (tragic from his perspective) element was there too. With the Genesis device, he could have ruled worlds or sectors or even the entire Quadrant, he could have had more power than on Earth, but he let his desire for revenge stand in his way.
In this context, compare his henchman, I think he was called Joachim, with Nero's 'Number One' Ayel. Joachim tried to remind Khan what he could do now with Genesis, while Ayel just did what his master wanted, another hollow character.
Such details make the difference between a vivid character like Khan and a clichée villain like Nero.