Never seen Cape Fear, but the theme always plays in my head when ever I see or think of a creeper .
Though De Niro is scary apperance wise, I think that's what makes Robert Mitchum scarier. He doesn't look like the sort of guy who'd come stalk you and your kids, so to speak, so the fact of someone being creepy that lookes normal scares me. A lot. I mean, De Niro (in Cape Fear) looks like he'd be a creeper, so you'd be able to get a gut-feeling if someone like him was around that would tell you "This guy's 'kinda creepy."
Also, Robert de Niro doesn't appear to get too close to the senator that convicted him in that version (the 90's one) as Mitchum did in the '62 version. From the clips I've seen of the 90's one, it only appears as if he gets "too close" to the daughter (WHO TOTALLY WANTS IT, LULZ). De Niro just really stared at the senator from across far distances, but as you can see in the trailer for the 1962 version, he gets very close.
I voted De Niro, based solely on first physical impression. Mitchum's performance was superb, however, his menace is more subtle, something you wouldn't notice until you've talked to him a while. Someone you wouldn't want buying you a drink and chatting you up at a bar, whereas De Niro's take exudes an underlying violence that one need just look at him to see. His Cady would impel someone to cross the street should he be coming the other way. I miss this De Niro. The sly subtle actor who could capture a moment with just a nod of his head rather than the bloated caricature he is today.
Both Roberts-es performances were superb and I would recommend anyone to take the time to watch both.