Why was Harry's condition so different from his father's?

First of all, I don't think Harry was affected by it so much at all. He seemed a bit weakened and had kind of a lesion at his throat. But both of those things are not something you couldn't hide (assuming Norman didn't get those things in such an obvious place as Harry did). The real problems didn't start until he tried to "heal" himself with the spider poison, which most likely had a contrary or otherwise unwanted effect due to Harry not having Richard Parker's blood.

The fact that it already started on Harry (and Norman) around the age of 20 doesn't necessarily mean that it grows steadily worse until the state we saw his father die from. And considering the rather few footage we saw from Norman Osborn, I don't find it hard to imagine him keeping on living and working in the state that we saw Harry in, and maybe hiding it a bit.

And also don't forget the scene near the end, when Harry is visited by this mystery guy in Ravencroft and looks relatively normal, especially compared to his previous appearance as Green Goblin. He simply explained it by saying something similar to

Well, it comes and goes.

So it's also quite likely that the illness doesn't develop entirely monotonous and that Norman Osborn had considerably worse days than those we saw him, which were to some degree public relations presences.

Perhaps the illness slowed down as Norman grew older, still affecting him, but at a slower rate. Or he could have slowed it down with help from Richard Parker.